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Synthetic Controllable Turbulence Using Robust Second Vorticity Confinement
Abstract
Capturing fine details of turbulence on a coarse grid is one of the main tasks in real‐time fluid simulation. Existing methods for doing this have various limitations. In this paper, we propose a new turbulence method that uses a refined second vorticity confinement method, referred to as robust second vorticity confinement, and a synthesis scheme to create highly turbulent effects from coarse grid. The new technique is sufficiently stable to efficiently produce highly turbulent flows, while allowing intuitive control of vortical structures. Second vorticity confinement captures and defines the vortical features of turbulence on a coarse grid. However, due to the stability problem, it cannot be used to produce highly turbulent flows. In this work, we propose a robust formulation to improve the stability problem by making the positive diffusion term to vary with helicity adaptively. In addition, we also employ our new method to procedurally synthesize the high‐resolution flow fields. As shown in our results, this approach produces stable high‐resolution turbulence very efficiently.
... This method applies the same on the whole region, and the value of is non-physical and has to be turned manually. There are adaptive methods, such as [17,18], which apply different confinement forces on different positions. These methods use current velocity and vorticity fields to generate the confinement force, which neglects the real vorticity dynamics. ...
... And a varying confinement force can severely affect the stability of LBM. Some work smooths the vorticity field or the confinement force [17,59], but smoothing obeys the original intention of increasing details. Hence, we propose a method tracking the magnitude of vorticity, which is more smoothed but not lack of details. ...
... This makes our method produce less noise. Furthermore, unlike other adaptive vorticity confinement methods [17,18], our method uses a tracked vorticity which is less probable to be affected by numerical dissipation. This is because motion of vorticity distribution function is weakly dependent on the momentum distribution function. ...
It is crucial to achieve high efficiency and to preserve fine-grid details in 3D interactive smoke simulation. In this paper, we present a vorticity preserving lattice Boltzmann method (VPLBM) to simulate high-resolution motion of smoke in real time. We design the method based on lattice Boltzmann method (LBM), which is parallelism-friendly, to ensure the efficiency on parallel computing devices such as graphic processing units (GPUs). To resolve the vorticity dissipation issue in LBM, we further propose an LBM-based vorticity transport method which tracks the magnitude of vorticity during the simulation. We apply vorticity confinement according to the tracked vorticity, and therefore, our method can preserve the detailed motion of smoke. Our method is forward-iterative and contains three weakly dependent distribution functions: two for thermal LBM and one for vorticity tracking. Finally, we show an implementation of a parallel smoke simulator integrating VPLBM method on a dual-GPU platform. Using a fast ray marching method, the simulator shows realistic visual effect and achieves 157.3 frames per second on a fine grid.
... Meanwhile, many turbulence synthesis [14] and guiding simulation [15] methods are proposed to obtain realistic results from the coarse simulation. Kim et al. [16] enabled a post-processing or procedural turbulence synthesis model by way of turbulent energy analysis, and He et al. [17] used a refined second vorticity confinement method to synthesize highly turbulent effects from the coarse grid. Nielsen and Bridson synthesized Fourier-based waves that match with the input to rapidly enhance the input wave animation with additional higher-frequency details in wave simulation [18]. ...
... To maintain the vortex structure in smoke, we introduce the helicity [17], an important physical property of turbulence. The helicity h of a gas flow is the integrated scalar product of the velocity field and the vorticity field: ...
This paper articulates a novel learning framework for both parameter estimation and detail enhancement for Eulerian gas based on data guidance. The key motivation of this paper is to devise a new hybrid, grid-based simulation that could inherit modeling and simulation advantages from both physically-correct simulation methods and data-driven methods, while combating existing difficulties exhibited in both approaches. We first employ a convolutional neural network to estimate the physical parameters of gaseous phenomena in Eulerian settings, then we can use the parameters to re-simulate for specific scenes. Next, a second CNN is adopted to reconstruct the high-resolution velocity field to guide a fast re-simulation on the finer grid, achieving richer details with little extra computational expense. From the perspective of physics-based simulation, our trained networks respect temporal coherence and physical constraints. From the perspective of the data-driven machine-learning approaches, our network design aims at extracting meaningful parameters and reconstructing realistic details. Additionally, our implementation based on parallel acceleration could enhance the computational performance of every involved module. Our comprehensive experiments confirm the controllability, effectiveness, and accuracy of our approach when producing various gaseous scenes with rich details for widespread graphics applications.
... By extending the original methods to multilevel, they managed to reproduce the energy cascading effects. He and Lau (2013) presented a scheme with better robustness to improve the stability of the secondary vorticity confinement by adjusting the positive diffusion term with the helicity adaptively. The approach managed to synthesize stable high-resolution turbulence flow field efficiently and allows intuitive control of vortical structures. ...
The instability and evolution mechanisms of propeller wakes are of vital significance to the development of next-generation propulsion devices with better hydrodynamic and noise performances. The temporal–spatial scales and the vortex details are important for the understanding of the vortex features and their dynamic responses to the propeller. In the present study, the vorticity confinement (VC) method was employed on the numerical simulations achieved by the improved delay detached eddy simulation with various advance coefficients to characterize the underlying features of wake flows. Comparisons were made between the results computed with and without the VC model from different perspectives. The analyses showed that the VC method captures more high-frequency power spectral density results as well as more small-scale vortical topology on the far downstream field based on the same spatial resolution and indicates the multi-scale interference on the tip vortex evolutionary trajectories. The VC method also elucidates rich small vortical structures with low advance coefficient and elliptical instability with high advance coefficient. This paper further widens our knowledge on the propeller wake evolution mechanisms and highlights the value of the VC method in the investigation of propeller wakes.
... 1. A parallel nested grid method that groups the vortex particles to decrease the number of vortex particles traversed during the velocity computation, thus reducing the computational cost; [16], and vorticity confinement [17][18][19] approaches. A common feature of the Eulerian method is that the fluid domain should be discretized in advance. ...
The Lagrangian vortex method has the advantage of producing highly detailed simulations of fluids such as turbulent smoke. However, this method has two problems: the construction of the velocity field from the vorticity field is inefficient, and handling the boundary condition is difficult. We present a pure Lagrangian vortex method, including a nested grid to accelerate the construction of the velocity field, and a novel boundary treatment method for the vorticity field. Based on a tree structure, the nested grid algorithm considerably improves the efficiency of the velocity computation while producing visual results that are comparable with the original flow. Based on the vortex-generating method, the least square method is used to compute the vorticity strength of the new vortex elements. Further, we consider the mutual influence between the generated vortex particles. We demonstrate our method’s benefits by using a vortex ring and various examples of interaction between the smoke and obstacles.
... HWPW11] proposed an adaptive vorticity coefficient method and obtained more turbulent details in smoke simulations. Later work improved this method[HL13] and further guaranteed the numeri-cal stability. Jamriska et al. [JFA * 15] proposed a texture synthesis approach based on flow-guided texture synthesis method. ...
Eulerian‐based smoke simulations are sensitive to the initial parameters and grid resolutions. Due to the numerical dissipation on different levels of the grid and the nonlinearity of the governing equations, the differences in simulation resolutions will result in different results. This makes it challenging for artists to preview the animation results based on low‐resolution simulations. In this paper, we propose a learning‐based flow correction method for fast previewing based on low‐resolution smoke simulations. The main components of our approach lie in a deep convolutional neural network, a grid‐layer feature vector and a special loss function. We provide a novel matching model to represent the relationship between low‐resolution and high‐resolution smoke simulations and correct the overall shape of a low‐resolution simulation to closely follow the shape of a high‐resolution down‐sampled version. We introduce the grid‐layer concept to effectively represent the 3D fluid shape, which can also reduce the input and output dimensions. We design a special loss function for the fluid divergence‐free constraint in the neural network training process. We have demonstrated the efficacy and the generality of our approach by simulating a diversity of animations deviating from the original training set. In addition, we have integrated our approach into an existing fluid simulation framework to showcase its wide applications.
... 21 . He et al. 22 used the second vorticity confinement to generate controllable turbulence. Moreover, synthetic turbulences were also utilized to add details on liquid surfaces. ...
In this paper, a novel method with good numerical stability is proposed from the perspective of energy preserving to alleviate the numerical dissipations in the advection step of Eulerian fluid simulation. The main idea is to measure the vorticity loss during advection, calculate the lost angular kinetic energy with a proposed scheme, and then synthesize a high‐frequency incompressible details field to compensate the lost energy in a way that is consistent with Kolmogorov's theory, which prevents the synthetic details from interfering with the existing fluid flow. The method works independently of the advection scheme and can be easily combined with other advection schemes to enhance the effect. It adds only 5% to 10% of the computational overhead while producing convincing fluid details without changing the overall behavior of the original flow.
Physics-based fluid simulation has played an increasingly important role in the computer graphics community. Recent methods in this area have greatly improved the generation of complex visual effects and its computational efficiency. Novel techniques have emerged to deal with complex boundaries, multiphase fluids, gas–liquid interfaces, and fine details. The parallel use of machine learning, image processing, and fluid control technologies has brought many interesting and novel research perspectives. In this survey, we provide an introduction to theoretical concepts underpinning physics-based fluid simulation and their practical implementation, with the aim for it to serve as a guide for both newcomers and seasoned researchers to explore the field of physics-based fluid simulation, with a focus on developments in the last decade. Driven by the distribution of recent publications in the field, we structure our survey to cover physical background; discretization approaches; computational methods that address scalability; fluid interactions with other materials and interfaces; and methods for expressive aspects of surface detail and control. From a practical perspective, we give an overview of existing implementations available for the above methods.
The advection step in grid‐based fluid simulation is prone to numerical dissipation, which results in loss of detail. How to improve the advection accuracy to preserve more fluid details is still challenging. On the other hand, a common way to enhance smoke details is to use vorticity confinement. However, most of the previous methods simply used a fine‐tuned scale factor ε to adjust the strength of the confinement force, which can only amplify existing vortex details and is easy to cause instability when ε is large. In this article, we proposed an adaptive vorticity confinement method, which does not suffer from the above problems, to compensate the vorticity loss during advection with little extra cost. The main idea is to first calculate a scale factor whose value depends on the vorticity loss during advection, and then use it to adaptively control the vorticity confinement force for vorticity compensation with high stability. The experiment results show the effectiveness and efficiency of our method.
Real-time fluid control is indispensable in computer animation, games, virtual reality, etc. In the field of Smoothed Particle Hydrodynamics (SPH) fluid control, the strategy of control force is often employed to control fluid particles; however, the artificial viscosity introduced by the control force would frequently lead to the loss of fine-scale details. Although the introduction of the low-pass filter can add back details, it may easily destroy the control target, and the control force method itself cannot make SPH fluid follow the fast-moving control target. Meanwhile, this type of method is computation intensive and time consuming. To remedy the above problems, this paper proposed a novel, interactive SPH fluid control framework with turbulent details. We run SPH fluid simulation on Compute Unified Device Architecture (CUDA) and greatly improve the efficiency of fluid control. The control particle with curvature framework was adapted in this paper. We specially designed spring forces to make the fluid match a fast-moving control target. Moreover, fine fluid details were preserved separately by calculating the fluid turbulence under control and the free fluid turbulence. This improved SPH fluid control can run in real time, which can enhance the visual quality of fluid animation as well. Our novel method can be applied in fluid animation with special control effects to guide fluid to form a target shape while greatly preserving the dynamic details of fluid. Various experiment results demonstrated the ability of our novel method.
In this paper, we propose an efficient approach for generating plausible smoke animation at interactive rates. Among a wide range of smoke animation approaches, our proposed approach simulates the behavior of gaseous phenomena such as turbulent smoke from a steam locomotive. Our method uses existing techniques for simulating smoke animation based on a particle system and extends them by introducing a simple yet efficient toroidal vortex to describe a more complex and turbulent behavior. The key idea is that vortex flows generated by torus-type smoke primitives are passively advected in a wind field to describe the turbulent flow of smoke.
Recruited by noncoding RNAs (ncRNAs) to specific genomic sites, polycomb repressive complexes 2 (PRC2) modify chromatin states in nearly all eukaryotes. The limited ncRNAs in Drosophila but abundant in mammals should have made PRC2 genes evolved significantly in Deuterostomia to adapt to the much increased ncRNAs. This study analyzes the evolution and coevolution of seven PRC2 genes in 29 Deuterostomia. These genes, previously assumed highly conserved, are found to have obtained multiple insertions in vertebrates and mammals and undergone significant positive selections in marsupials and prosimians, indicating adaptions to substantially increased lncRNAs (long noncoding RNAs) in mammals and in primates. Some insertions occur notably in homologous sequences of human nonsense-mediated decay (NMD) transcripts. Moreover, positive selections and signals of convergent evolution imply the independent increase of lncRNAs in mammals and in primates. Coevolutionary analysis reveals that patterns of interaction between PRC2 proteins have also much evolved from vertebrates to mammals, indicating adaptation at the protein complex level. The potential functions of mammalian-specific insertions and NMD transcripts deserve further experimental examination.
We present an up-to-date survey on physically-based smoke simulation. Physically-based method becomes predominant in smoke simulation in computer graphics community. It prevails over traditional methods for its plausible visual effect. Significant results have been carried out over past two decades. We give a latest overview of state-of-the-art of smoke simulation and also compare various techniques according to their characteristics. We discuss several issues in terms of computational efficiency, numerical stability, numerical dissipation, and runtime performance. A number of open challenging problems are also addressed for further exploration.
Numerical dissipation acts as artificial viscosity to make smoke viscous. Reducing numerical dissipation is able to recover visual details smeared out by the numerical dissipation. Great efforts have been devoted to suppress the numerical dissipation in smoke simulation in the past few years. In this paper we investigate methods of combating the numerical dissipation. We describe visual consequences of the numerical dissipation and explore sources that introduce the numerical dissipation into course of smoke simulation. Methods are investigated from various aspects including grid variation, high-order advection, sub-grid compensation, invariant conservation, and particle-based improvement, followed by discussion and comparison in terms of visual quality, computational overhead, ease of implementation, adaptivity, and scalability, which leads to their different applicability to various application scenarios.
We present a novel procedural synthesis method to improve small-scale turbulence details for controllable smoke animation constrained by shapes and paths. In order to enhance fluid details without introducing unpleasing fluid control effects, we propose a spatial–temporal varying synthesis parameter to control turbulence behaviors and compute it from control force and the vorticity velocity. Our approach can control enhanced turbulence behaviors efficiently and produces visually plausible realistic fine-scale details while reducing artifacts of large-scale noises on fluid control. We compare our algorithm to existing procedural synthesis ones to validate its efficiency and controllability. Copyright © 2014 John Wiley & Sons, Ltd.
While small-scale fluid details are crucial elements for the creation of visually pleasing fluid animations, their synthesis often requires heavy computation with traditional grid-based fluid simulation methods. This paper proposes a novel method for enhancing the appearance of small-scale details through frequency-domain analysis. Different from previous work, our method detects and improves fluid details in the frequency-domain via lifting wavelet decomposition. Based on a coarse-to-fine mechanism, the lifting wavelet composition first transforms the velocity in a fine grid into the frequency domain. Next, the velocity field is enhanced separately for different frequency bands. A novel velocity fusion method is developed for the enhancement of low-frequency parts. On the other hand, high-frequency parts are enhanced using a specially designed vorticity confinement method. Finally, the application of the inverse lifting wavelet transform determines the final velocity field with increased fine details. Our method can generate perceptually interesting fluid details, matching human visual perception theory. The results of various experiments validate the effectiveness and efficiency of our method. Copyright © 2014 John Wiley & Sons, Ltd.
In this work, we describe a method that automates the sampling and control of gaseous fluid simulations. Several recent approaches have provided techniques for artists to generate high-resolution simulations based on a low-resolution simulation. However, often in applications the overall flow in the low-resolution simulation that an animator observes and intends to preserve is composed of even lower frequencies than the low resolution itself. In such cases, attempting to match the low-resolution simulation precisely is unnecessarily restrictive. We propose a new sampling technique to efficiently capture the overall flow of a fluid simulation, at the scale of user’s choice, in such a way that the sampled information is sufficient to represent what is virtually perceived and no more. Thus, by applying control based on the sampled data, we ensure that in the resulting high-resolution simulation, the overall flow is matched to the low-resolution simulation and the fine details on the high resolution are preserved. The samples we obtain have both spatial and temporal continuity that allows smooth keyframe matching and direct manipulation of visible elements such as smoke density through temporal blending of samples. We demonstrate that a user can easily configure a simulation with our system to achieve desired results.
A new ‘‘vorticity confinement’’ method is described which involves adding a term to the momentum conservation equations of fluid dynamics. This term depends only on local variables and is zero outside vortical regions. The partial differential equations with this extra term admit solutions that consist of Lagrangian-like confined vortical regions, or covons, in the shape of two-dimensional (2-D) vortex ‘‘blobs’’ and three-dimensional (3-D) vortex filaments, which convect in a constant external velocity field with a fixed internal structure, without spreading, even if the equations contain diffusive terms. Solutions of the discretized equations on a fixed Eulerian grid show the same behavior, in spite of numerical diffusion. Effectively, the new term, together with diffusive terms, constitute a new type of regularization of the inviscid equations which appears to be very useful in the numerical solution of flow problems involving thin vortical regions. The discretized Euler equations with the extra term can be solved on fairly coarse, Eulerian computational grids with simple low-order (first- or second-) accurate numerical methods, but will still yield concentrated vortices which convect without spreading due to numerical diffusion. Since only a fixed grid is used with local variables, the vorticity confinement method is quite general and can automatically accommodate changes in vortex topology, such as merging. Applications are presented for incompressible flow in 3D, where pairs of thin vortex rings interact and, in some cases, merge.
We introduce a simple turbulence model for smoke animation, qualitatively capturing the transport, diffusion, and spectral cascade of turbulent energy unresolved on a typical simulation grid. We track the mean kinetic energy per octave of turbulence in each grid cell, and a novel "net rotation" variable for modeling the self-advection of turbulent eddies. These additions to a standard fluid solver drive a procedural post-process, layering plausible dynamically evolving turbulent details on top of the large-scale simulated motion. Finally, to make the most of the simulation grid before jumping to procedural sub-grid models, we propose a new multistep predictor to alleviate the nonphysical dissipation of angular momentum in standard graphics fluid solvers.
We propose a novel approach to guiding of Eulerian-based smoke animations through coupling of simulations at different grid resolutions. Specifically we present a variational formulation that allows smoke animations to adopt the low-frequency features from a lower resolution simulation (or non-physical synthesis), while simultaneously developing higher frequencies. The overall motivation for this work is to address the fact that art-direction of smoke animations is notoriously tedious. Particularly a change in grid resolution can result in dramatic changes in the behavior of smoke animations, and existing methods for guiding either significantly lack high frequency detail or may result in undesired features developing over time. Provided that the bulk movement can be represented satisfactorily at low resolution, our technique effectively allows artists to prototype simulations at low resolution (where computations are fast) and subsequently add extra details without altering the overall "look and feel". Our implementation is based on a customized multi-grid solver with memory-efficient data structures.
The back and forth error compensation and correction (BFECC) method advects the solution forward and then backward in time. The result is compared to the original data to estimate the error. Although inappropriate for parabolic and other non-reversible par- tial differential equations, it is useful for often troublesome advec- tion terms. The error estimate is used to correct the data before advection raising the method to second order accuracy, even though each individual step is only first order accurate. In this paper, we rewrite the MacCormack method to illustrate that it estimates the error in the same exact fashion as BFECC. The difference is that the MacCormack method uses this error estimate to correct the already computed forward advected data. Thus, it does not require the third advection step in BFECC reducing the cost of the method while still obtaining second order accuracy in space and time. Recent work re- placed each of the three BFECC advection steps with a simple first order accurate unconditionally stable semi-Lagrangian method yield- ing a second order accurate unconditionally stable BFECC scheme. We use a similar approach to create a second order accurate uncon- ditionally stable MacCormack method.
We describe a method for controlling smoke simulations through user-specified keyframes. To achieve the desired behavior, a continuous quasi-Newton optimization solves for appropriate "wind" forces to be applied to the underlying velocity field throughout the simulation. The cornerstone of our approach is a method to efficiently compute exact derivatives through the steps of a fluid simulation. We formulate an objective function corresponding to how well a simulation matches the user's keyframes, and use the derivatives to solve for force parameters that minimize this function. For animations with several keyframes, we present a novel multipleshooting approach. By splitting large problems into smaller overlapping subproblems, we greatly speed up the optimization process while avoiding certain local minima.
Turbulent vortices in fluid flows are crucial for a visually interesting appearance. Although there has been a significant amount of work on turbulence in graphics recently, these algorithms rely on the underlying simulation to resolve the flow around objects. We build upon work from classical fluid mechanics to design an algorithm that allows us to accurately precompute the turbulence being generated around an object immersed in a flow. This is made possible by modeling turbulence formation based on an averaged flow field, and relying on universal laws describing the flow near a wall. We precompute the confined vorticity in the boundary layer around an object, and simulate the boundary layer separation during a fluid simulation. Then, a turbulence model is used to identify areas where this separated layer will transition into actual turbulence. We sample these regions with vortex particles, and simulate the further dynamics of the vortices based on these particles. We will show how our method complements previous work on synthetic turbulence, and yields physically plausible results. In addition, we demonstrate that our method can efficiently compute turbulent flows around a variety of objects including cars, whisks, as well as boulders in a river flow. We can even apply our model to precomputed static flow fields, yielding turbulent dynamics without a costly simulation.
It is usually difficult to resolve the fine details of turbulent flows, especially when targeting real-time applications. We present a novel, scalable turbulence method that uses a realistic energy model and an efficient particle representation that allows for the accurate and robust simulation of small-scale detail. We compute transport of turbulent energy using a complete two-equation k-ε model with accurate production terms that allows us to capture anisotropic turbulence effects, which integrate smoothly into the base flow. We only require a very low grid resolution to resolve the underlying base flow. As we offload complexity from the fluid solver to the particle system, we can control the detail of the simulation easily by adjusting the number of particles, without changing the large scale behavior. In addition, no computations are wasted on areas that are not visible. We demonstrate that due to the design of our algorithm it is highly suitable for massively parallel architectures, and is able to generate detailed turbulent simulations with millions of particles at high framerates.
We describe a novel method for controlling physics-based fluid simulations through gradient-based nonlinear optimization. Using a technique known as the adjoint method, derivatives can be computed efficiently, even for large 3D simulations with millions of control parameters. In addition, we introduce the first method for the full control of free-surface liquids. We show how to compute adjoint derivatives through each step of the simulation, including the fast marching algorithm, and describe a new set of control parameters specifically designed for liquids.
We present a novel technique for the animation of turbulent fluids by coupling a procedural turbulence model with a numerical fluid solver to introduce subgrid-scale flow detail. From the large-scale flow simulated by the solver, we model the production and behav- ior of turbulent energy using a physically motivated energy model. This energy distribution is used to synthesize an incompressible tur- bulent velocity field, whose features show plausible temporal be- havior through a novel Lagrangian approach for advected noise. The synthesized turbulent flow has a dynamical effect on the large- scale flow, and produces visually plausible detailed features on both gaseous and free-surface liquid flows. Our method is an order of magnitude faster than full numerical simulation of equivalent reso- lution, and requires no manual direction.
Vorticity confinement reintroduces the small scale detail lost when using efficient semi-Lagrangian schemes for simulating smoke and fire. However, it only amplifies the existing vorticity, and thus can be insufficient for highly turbulent effects such as explosions or rough water. We introduce a new hybrid technique that makes synergistic use of Lagrangian vortex particle methods and Eulerian grid based methods to overcome the weaknesses of both. Our approach uses vorticity confinement itself to couple these two methods together. We demonstrate that this approach can generate highly turbulent effects unachievable by standard grid based methods, and show applications to smoke, water and explosion simulations.
Back and Forth Error Compensation and Correction (BFECC) was recently developed for interface computation using a level set method. We show that BFECC can be applied to reduce dissipation and diffusion encountered in a variety of advection steps, such as velocity, smoke density, and image advections on uniform and adaptive grids and on a triangulated surface. BFECC can be implemented trivially as a small modification of the first-order upwind or semi-Lagrangian integration of advection equations. It provides second-order accuracy in both space and time. When applied to level set evolution, BFECC reduces volume loss significantly. We demonstrate the benefits of this approach on image advection and on the simulation of smoke, bubbles in water, and the highly dynamic interaction between water, a solid, and air. We also apply BFECC to dye advection to visualize vector fields.
In this paper, we propose a new approach to numerical smoke simulation for computer graphics applications. The method proposed here exploits physics unique to smoke in order to design a numerical method that is both fast and efficient on the relatively coarse grids traditionally used in computer graphics applications (as compared to the much finer grids used in the computational fluid dynamics literature). We use the inviscid Euler equations in our model, since they are usually more appropriate for gas modeling and less computationally intensive than the viscous NavierStokes equations used by others. In addition, we introduce a physically consistent vorticity confinement term to model the small scale rolling features characteristic of smoke that are absent on most coarse grid simulations. Our model also correctly handles the interaction of smoke with moving objects. Keywords: Smoke, computational fluid dynamics, Navier-Stokes equations, Euler equations, Semi-Lagrangian methods, stable fluids, vorticity confinement, participating media 1
It is usually difficult to resolve the fine details of turbulent flows, especially when targeting real-time applications. We present a novel, scalable turbulence method that uses a realistic energy model and an efficient particle representation that allows for the accurate and robust simulation of small-scale detail. We compute transport of turbulent energy using a complete two-equation k-e model with accurate production terms that allows us to capture anisotropic turbulence effects, which integrate smoothly into the base flow. We only require a very low grid resolution to resolve the underlying base flow. As we offload complexity from the fluid solver to the particle system, we can control the detail of the simulation easily by adjusting the number of particles, without changing the large scale behavior. In addition, no computations are wasted on areas that are not visible. We demonstrate that due to the design of our algorithm it is highly suitable for massively parallel architectures, and is able to generate detailed turbulent simulations with millions of particles at high framerates.
Turbulent vortices in fluid flows are crucial for a visually interesting appearance. Although there has been a significant amount of work on turbulence in graphics recently, these algorithms rely on the underlying simulation to resolve the flow around objects. We build upon work from classical fluid mechanics to design an algorithm that allows us to accurately precompute the turbulence being generated around an object immersed in a flow. This is made possible by modeling turbulence formation based on an averaged flow field, and relying on universal laws describing the flow near a wall. We precompute the confined vorticity in the boundary layer around an object, and simulate the boundary layer separation during a fluid simulation. Then, a turbulence model is used to identify areas where this separated layer will transition into actual turbulence. We sample these regions with vortex particles, and simulate the further dynamics of the vortices based on these particles. We will show how our method complements previous work on synthetic turbulence, and yields physically plausible results. In addition, we demonstrate that our method can efficiently compute turbulent flows around a variety of objects including cars, whisks, as well as boulders in a river flow.We can even apply our model to precomputed static flow fields, yielding turbulent dynamics without a costly simulation.
Many flows of interest are characterized by large regions of concentrated (and turbulent) vortical structures that persist and can convect over long distances. Flows of this nature include those associated with aircraft, but also include flows associated with ships, automobiles, bridges, and buildings. Conventional CFD methods tend to dissipate vortical structures, degrading the overall accuracy of the computed flow. This dissipation can be reduced through the use of fine grids, but at the expense of greatly increased computational demands. In addition, no conventional CFD method produces the unsteady chaotic flow associated with turbulence except on extremely fine grids and in very small regions. The vorticity confinement method prevents the dissipation of vortical structures on coarse grids, and approximately produces the unsteady small-scale features (down to grid-cell scale) associated with physical turbulence. In this paper, vorticity confinement is used to model a turbulent wake behind a cylinder. Comparisons with data demonstrate the potential of vorticity confinement to predict mean wake flow and Reynolds stresses accurately and efficiently, even on a coarse grid. In addition, computations are performed on a realistic ship configuration; the resulting velocity field and bow vortex trajectory are shown to agree well with wind tunnel measurements.
A numerical method for computing three-dimensional, unsteady incompressible flows is presented. The method is a predictor-corrector technique combined with a fractional step method. Each time step is advanced in three sub-steps. The novel feature of the present scheme is that the Poisson equation for the pressure is solved only at the final sub-step resulting in substantial savings in computing time. It is shown that the method allows a larger CFL number and reduces the computing cost without loss of accuracy by satisfying the continuity equation only at the last sub-step. Numerical solutions for the decaying vortices and flow over a backward-facing step are obtained and compared with analytical and other numerical results.
The second vorticity confinement scheme proposed by Steinhoff is analysed in detail. First, starting from the 1D linear transport equation applied to a pulse, various formulations for the confinement are compared. The linear 2nd-order schemes (Warming-Beam and Lax–Wendroff schemes) give oscillatory solutions, while the nonlinear confinements of same accuracy behave as limiters with artificial compression. Not only these 2nd-order schemes with confinement conserve the pulse as accurately as a 3rd-order one for identical and sufficiently fine grids, but they remain stable with a global negative diffusion which allows them to conserve the pulse endlessly concentrated over 5–8 mesh cells in the computation, although the form of the equations is then lowered to 1st-order. Application of the energy method for stability analysis indicates that the signal relaxes towards a constant energy solution, for which the energy brought in by the anti-diffusive confinement is balanced by the energy removed from the solution by the diffusive terms. Application to the Euler equations for the advection of a 2D vortex proves that a similar approach can be applied to nonlinear problems. The most appropriate formulation of compressible vorticity confinement is to apply it identically to the incompressible formulation, i.e. without source term in the energy conservation equation.
In this work, we describe an automated method for directing the control of a high resolution gaseous fluid simulation based on the results of a lower resolution preview simulation. Small variations in accuracy between low and high resolution grids can lead to divergent simulations, which is problematic for those wanting to achieve a desired behavior. Our goal is to provide a simple method for ensuring that the high resolution simulation matches key properties from the lower resolution simulation. We first let a user specify a fast, coarse simulation that will be used for guidance. Our automated method samples the data to be matched at various positions and scales in the simulation, or allows the user to identify key portions of the simulation to maintain. During the high resolution simulation, a matching process ensures that the properties sampled from the low resolution simulation are maintained. This matching process keeps the different resolution simulations aligned even for complex systems, and can ensure consistency of not only the velocity field, but also advected scalar values. Because the final simulation is naturally similar to the preview simulation, only minor controlling adjustments are needed, allowing a simpler control method than that used in prior keyframing approaches.
Momentum conservation has long been used as a design principle for solid simulation (e.g. collisions between rigid bodies, mass-spring elastic and damping forces, etc.), yet it has not been widely used for fluid simulation. In fact, semi-Lagrangian advection does not conserve momentum, but is still regularly used as a bread and butter method for fluid simulation. In this paper, we propose a modification to the semi-Lagrangian method in order to make it fully conserve momentum. While methods of this type have been proposed earlier in the computational physics literature, they are not necessarily appropriate for coarse grids, large time steps or inviscid flows, all of which are common in graphics applications. In addition, we show that the commonly used vorticity confinement turbulence model can be modified to exactly conserve momentum as well. We provide a number of examples that illustrate the benefits of this new approach, both in conserving fluid momentum and passively advected scalars such as smoke density. In particular, we show that our new method is amenable to efficient smoke simulation with one time step per frame, whereas the traditional non-conservative semi-Lagrangian method experiences serious artifacts when run with these large time steps, especially when object interaction is considered.
Abstract We propose a fast and effective technique to improve sub-grid visual details of the grid based fluid simulation. Our method procedurally synthesizes the flow fields coming from the incompressible Navier-Stokes solver and the vorticity fields generated by vortex particle method for sub-grid turbulence. We are able to efficiently animate smoke which is highly turbulent and swirling with small scale details. Since this technique does not solve the linear system in high-resolution grids, it can perform fluid simulation more rapidly. We can easily estimate the influence of turbulent and swirling effect to the fluid flow.
Abstract We develop a new Lagrangian primitive, named Langevin particle, to incorporate turbulent flow details in fluid simulation. A group of the particles are distributed inside the simulation domain based on a turbulence energy model with turbulence viscosity. A particle in particular moves obeying the generalized Langevin equation, a well known stochastic differential equation that describes the particle's motion as a random Markov process. The resultant particle trajectory shows self-adapted fluctuation in accordance to the turbulence energy, while following the global flow dynamics. We then feed back Langevin forces to the simulation based on the stochastic trajectory, which drive the flow with necessary turbulence. The new hybrid flow simulation method features nonrestricted particle evolution requiring minimal extra manipulation after initiation. The flow turbulence is easily controlled and the total computational overhead of enhancement is minimal based on typical fluid solvers.
A new version of a computational method, Vorticity Confinement, is described. Vorticity Confinement has been shown to efficiently treat thin features in multi-dimensional incompressible fluid flow, such as vortices and streams of passive scalars, and to convect them over long distances with no spreading due to numerical errors. Outside the features, where the flow is irrotational or the scalar vanishes, the method automatically reduces to conventional discretized finite difference fluid dynamic equations. The features are treated as a type of weak solution and, within the features, a nonlinear difference equation, as opposed to finite difference equation, is solved that does not necessarily represent a Taylor expansion discretization of a simple partial differential equation (PDE). The approach is similar to artificial compression and shock capturing schemes, where conservation laws are satisfied across discontinuities. For the features, the result of this conservation is that integral quantities such as total amplitude and centroid motion are accurately computed. Basically, the features are treated as multi-dimensional nonlinear discrete solitary waves that live on the computational lattice. These obey a “confinement” relation that is a generalization to multiple dimensions of 1-D discontinuity capturing schemes. A major point is that the method involves a discretization of a rotationally invariant operator, rather than a composition of separate 1-D operators, as in conventional discontinuity capturing schemes. The main objective of this paper is to introduce a new formulation of Vorticity Confinement that, compared to the original formulation, is simpler, allows more detailed analysis, and exactly conserves momentum for vortical flow. First, a short critique of conventional methods for these problems is given. The basic new method is then described. Finally, analysis of the new method and initial results are presented.
A recently developed method is described to propagate short wave equation pulses over indefinite distances and through regions of varying indices of refraction, including multiple reflections. The method, “Wave Confinement”, utilizes a newly developed nonlinear partial differential equation (pde) that propagates basis functions according to the wave equation. These basis functions are generated as stable solitary waves where the discretized equation can be solved without any numerical dissipation. The method can also be used to solve for harmonic waves in the high frequency (Eikonal) limit, including multiple arrivals. The solution involves discretizing the wave equation on a uniform Eulerian grid and adding a simple nonlinear “Confinement” term. This term does not change the amplitude (integrated through each point on the pulse surface) or the propagation velocity, or arrival time, and yet results in capturing the waves as thin surfaces that propagate as thin nonlinear solitary waves and remain ∼2–3 grid cells in thickness indefinitely with no numerical spreading. A new feature described in this paper involves computing scattering of short pulses from complex objects such as complete aircraft. A simple “immersed surface” approach is used, that utilizes the same uniform grid as the propagation and avoids complex, body fitted or adaptive grid schemes.The new method should be useful in areas of wave propagation, from radar scattering and long distance communications to cell phone transmission.
Turbulence modeling has recently drawn many attentions in fluid animation to generate small-scale rolling features. Being one of the widely adopted approaches, vorticity confinement method re-injects lost energy dissipation back to the flow. However, previous works suffer from deficiency when large vorticity coefficient ε is used, due to the fact that constant ε is applied all over the simulated domain. In this paper, we propose a novel approach to enhance the visual effect by employing an adaptive vorticity confinement which varies the strength with respect to the helicity instead of a user-defined constant. To further improve fine details in turbulent flows, we are not only applying our proposed vorticity confinement to low-resolution grid, but also on a finer grid to generate sub-grid level turbulence. Since the incompressible Navier–Stokes equations are solved only in low-resolution grid, this saves a significant amount of computation. Several experiments demonstrate that our method can produce realistic smoke animation with enhanced turbulence effects in real-time. Copyright © 2011 John Wiley & Sons, Ltd.
Fluid animation practitioners face great challenges from the complexity of flow dynamics and the high cost of numerical simulation. A major hindrance is the uncertainty of fluid behavior after simulation resolution increases and extra turbulent effects are added. In this paper, we propose to regulate fluid animations with predesigned flow patterns. Animators can design their desired fluid behavior with fast, low-cost simulations. Flow patterns are then extracted from the results by the Lagrangian Coherent Structure (LCS) that represents major flow skeleton. Therefore, the final high-quality animation is confined towards the designed behavior by applying the patterns to drive high-resolution and turbulent simulations. The pattern regulation is easily computed and achieves controllable variance in the output. The method makes it easy to design special fluid effects, which increases the usability and scalability of various advanced fluid modeling technologies.
We present a physics-based simulation method for animating sand. To allow for efficiently scaling up to large volumes of sand, we abstract away the individual grains and think of the sand as a continuum. In particular we show that an existing water simulator can be turned into a sand simulator with only a few small additions to account for inter-grain and boundary friction.We also propose an alternative method for simulating fluids. Our core representation is a cloud of particles, which allows for accurate and flexible surface tracking and advection, but we use an auxiliary grid to efficiently enforce boundary conditions and incompressibility. We further address the issue of reconstructing a surface from particle data to render each frame.
We present a novel wavelet method for the simulation of fluids at high spatial resolution. The algorithm enables large- and small-scale detail to be edited separately, allowing high-resolution detail to be added as a post-processing step. Instead of solving the Navier-Stokes equations over a highly refined mesh, we use the wavelet decomposition of a low-resolution simulation to determine the location and energy characteristics of missing high-frequency components. We then synthesize these missing components using a novel incompressible turbulence function, and provide a method to maintain the temporal coherence of the resulting structures. There is no linear system to solve, so the method parallelizes trivially and requires only a few auxiliary arrays. The method guarantees that the new frequencies will not interfere with existing frequencies, allowing animators to set up a low resolution simulation quickly and later add details without changing the overall fluid motion.
Fluid Simulation for Computer Graphics. A K Peters
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] BRIDSON R.: Fluid Simulation for Computer Graphics. A K Peters, Elsevier Science B.V., Amsterdam, France, 2008.
Fluid control using the adjoint method
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Fluid Simulation for Computer Graphics.A KPeters Elsevier Science B
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