Article

# Synthetic Controllable Turbulence Using Robust Second Vorticity Confinement

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## 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.

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... 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. ...
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... 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: ...
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... 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. ...
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... 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. ...
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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.
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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.
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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.
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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.
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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.
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Fluid control using the adjoint method
• McNamara