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Unified strategy of supermesh generation for planar, cylindrical, and spherical non-conformal interfaces by using 2-D intersection algorithm
Abstract
Aimed at decreasing the complexity of calculating the intersection of a pair of overlapped interfaces, this paper presents an efficient unified strategy to generate a supermesh for planar, cylindrical, and spherical non-conformal interfaces uniquely, which retains the computational efficiency of a 2-D intersection algorithm. The coordinate transformations for both the cylindrical and spherical interfaces are considered because the nodes of both types of interfaces can be described by two variable coordinates and a constant coordinate. The coordinate transformation of the spherical interfaces is performed by combining the Gnomonic projection and notion of rigid rotation. This task is incorporated in the local-supermeshing approach to generate the supermesh, which is employed as an auxiliary mesh to realize one-to-one addressing between the cells on both sides of the interfaces. Tests are performed to determine the pure geometric error of the supermeshing approach, and the results show the method does not induce additional geometric error. Besides, the accuracy and conservation of the fluxes when applying the supermeshing approach in a particular solver are studied. The results of the full-cycle unsteady simulation of internal combustion indicate the feasibility to applying the proposed method to realistic numerical problems.
... In this context, the supermesh-based sliding interfaces method [8] is combined with the particle tracking process to tackle the interfaces-crossing issue in the two-way coupling method for the flows with a dilute disperse phase in serial computing. This basic algorithm is implemented in our in-house code which is based on the unstructured finite volume method. ...
... In this scenario, based on the author's previous work [8,16], a novel and robust parallel algorithm for the Eulerian-Lagrangian approach crossing sliding mesh interfaces is provided in detail for two-way coupling in this work. This algorithm has no constraints on the domain partition schemes and can well handle the problem of particles crossing sliding non-conformal interfaces in parallel computing, which is suitable for a wide range of engineering applications. ...
... In the author's previous work [16], a highly scalable and robust parallel algorithm to handle the data transmission across the sliding nonconformal interfaces was developed based on an efficient supermesh method [25,26], which has no constraints on the domain decomposition schemes and adapts to practical engineering simulation with complex geometries. Besides, based on the supermesh generation method proposed in the author's previous work [8], the geometric calculation problem of particles crossing non-conformal curved interface cases such as cylinder and spherical interfaces can also be handled. ...
Numerical simulations of flows with dilute disperse phase play an important role in a wide range of industrial applications. The most commonly used technique for solving such problems is the Eulerian-Lagrangian approach, in which individual particles are tracked inside the domain. However, the use of sliding and moving mesh in complex engineering applications poses more challenges for the parallelization of the Eulerian-Lagrangian method in the two-way coupling. In this context, this manuscript presents the parallel algorithm for tracking Lagrangian particles crossing sliding non-conformal interfaces in a mixed Eulerian-Lagrangian CFD algorithm, which is based on a parallel supermesh method introduced recently for the handling of sliding mesh in large-scale parallel computing (Y. Xiao and P.J. Ming, Jour. Computat. Phys., 2022). In the proposed parallel algorithm, critical problems such as geometric calculation for particles across non-conformal mesh interfaces and the dynamic communication for particle data can be handled based on the one-to-one addressing constructed by the supermesh method introduced in the author’s previous work. Further, a robust and easy-to-implement algorithm is also provided for particle communication caused by mesh moving. All methodologies are integrated and implemented for parallel computation obtaining good robustness and consistency. Specific examples are solved to examine the performance of this parallel strategy when applied to practical engineering problems.
... In this paper, we propose some solutions to the scalability limitations of the sliding non-conformal interface technology employed for the simulation of practical engineering problems. As an extension to the author's previous work [23], the research effort described in this paper has been focused primarily on the development of a highly scalable and robust parallel algorithm to handle the data transmission across the sliding non-conformal interfaces, which has no constraints on the domain decomposition schemes and adapts to practical engineering simulation with complex geometries. This parallel algorithm is mainly designed for the unstructured flow solver execution on a distributed-memory computer with multi-processors, each of them stores only the mesh and the flow field data of the assigned sub-domains. ...
... In the first place of this section, the basis of the supermesh is briefly presented followed by a description of the implementation of the local supermeshing approach. The detailed introduction can refer to the author's previous work [23]. Subsequently, the flux-conservation treatment using supermesh is described. ...
... However, unlike in the case of planar interfaces, the calculation of the intersection (as the step 6 in Algorithm 1) might be hindered for curved interface cases such as cylindrical and spherical interfaces, because the overlapped interface elements might be not in the same plane in 3-D space. This geometric intersection problem has been studied in the author's previous work [23] where a coordinate transformation was proposed to project the 3-D interface elements into 2-D space, and 2-D clipping algorithm is then implemented to calculate the intersection of the supermesh for both spherical and cylindrical interfaces. This operation can extremely decrease the geometric error of supermesh generation for spherical and cylindrical interfaces. ...
Handling of non-conformal interfaces communication is one of the challenges from which the parallelization of multi-zone unstructured grids technology suffers. Especially for dynamic mesh simulation, changing dynamic communication patterns induced by the grids relative motion requires data to be correctly transferred across discrete non-conformal interfaces at every time step. To overcome the challenges at extreme scales in this paper we attempt to design the parallel algorithm in such a way that it enhances the scalability of the sliding mesh method implemented in the simulation of practical engineering problems with complex geometries. In the proposed parallel algorithm, the issue of changing dynamic interface communication is handled by a scalable and robust parallel supermeshing algorithm which has no constraints on the domain partition schemes and is adapted to complex practical engineering simulation. Besides, a unified cell-based communication map adapting to parallelized matrixes solvers is dynamically reconstructed by assembling both the inner-boundary communication map and interface communication map, which greatly improves the robustness and scalability of the sliding mesh algorithm executed on the parallel CFD code. All methodologies are integrated and implemented for parallel computation obtaining good scalability and computational efficiency. Specific examples are solved to analyze the conservation, scalability and robustness of the parallelized interface approach and finally, the full-cycle unsteady simulation of a four-stroke engine is tested to evaluate the performance of this parallel strategy when applied to practical engineering problems.
With the arrival of the digital era of manufacturing, numerical simulation technology plays an important role as a powerful research tool in all aspects of the optimization design of internal combustion engines. The working process of internal combustion engines is a complex process of coupling of flow, heat transfer and chemical reaction, and there are also the effects of multiple moving components such as valves and piston, making the three-dimensional thermal performance simulation of internal combustion engines more complicated. In the context of localization and self-reliance of CAE software, the development of CFD numerical simulation software and its key generic algorithms for internal combustion engines is of strategic significance for aerospace, aeronautics, and marine engineering.
In this study, a numerical calculation method for in-cylinder flow and spray combustion under the effect of inlet and exhaust gas flow and its full-flow general parallel code are developed based on in-house platform GTEA (General Transport Equation Analyzer), a general equation solver independently developed by the laboratory.
随着制造业数字化时代的到来，数值仿真技术作为一种强有力的研究手段在内燃机优化设计各个环节中发挥着重要作用。内燃机的缸内过程是流动、传热和化学反应耦合的复杂作用过程，而且还存在气阀及活塞等多组运动部件的影响，使得内燃机三维热力性能仿真更加复杂。在CAE工业软件国产自主化的迫切需求下，开发内燃机相关的CFD数值仿真软件及其关键性通用算法对航空、航天、航海工程具有重要的战略意义。
本文基于课题组自主研发的通用方程求解器GTEA(General Transport Equation Analyzer)，发展了一种进排气影响下的缸内流动与喷雾燃烧数值计算方法及其全流程通用并行数值模拟程序。
An efficient, local, explicit, second-order, conservative interpolation algorithm between spherical meshes is presented. The cells composing the source and target meshes may be either spherical polygons or latitude–longitude quadrilaterals. Second-order accuracy is obtained by piece-wise linear finite-volume reconstruction over the source mesh. Global conservation is achieved through the introduction of a “supermesh”, whose cells are all possible intersections of source and target cells. Areas and intersections are computed exactly to yield a geometrically exact method. The main efficiency bottleneck caused by the construction of the supermesh is overcome by adopting tree-based data structures and algorithms, from which the mesh connectivity can also be deduced efficiently.
The theoretical second-order accuracy is verified using a smooth test function and pairs of meshes commonly used for atmospheric modelling. Experiments confirm that the most expensive operations, especially the supermesh construction, have O(NlogN) computational cost. The method presented is meant to be incorporated in pre- or post-processing atmospheric modelling pipelines, or directly into models for flexible input/output. It could also serve as a basis for conservative coupling between model components, e.g., atmosphere and ocean.
An efficient, local, explicit, second-order, conservative interpolation algorithm between spherical meshes is presented. The cells composing the source and target meshes may be either spherical polygons or longitude–latitude quadrilaterals. Second-order accuracy is obtained by piecewise-linear finite volume reconstruction over the source mesh. Global conservation is achieved through the introduction of a supermesh, whose cells are all possible intersections of source and target cells. Areas and intersections are computed exactly to yield a geometrically exact method. The main efficiency bottleneck caused by the construction of the supermesh is overcome by adopting tree-based data structures and algorithms, from which the mesh connectivity can also be deduced efficiently.
The theoretical second-order accuracy is verified using a smooth test function and pairs of meshes commonly used for atmospheric modelling. Experiments confirm that the most expensive operations, especially the supermesh construction, have O(NlogN) computational cost. The method presented is meant to be incorporated in pre- or post-processing atmospheric modelling pipelines, or directly into models for flexible input/output. It could also serve as a basis for conservative coupling between model components, e.g. atmosphere and ocean.
A conservative remapping method is developed to improve the accuracy of data exchange on the patched
(mismatched) grid interface. Linear and quadratic polynomials are tested for the reconstruction of the conservative variables on the interface. Remapping methods with different accuracies are compared. Results show that the combination of the linear reconstruction and the weighted essentially nonoscillatory stencil selection has the best balance of accuracy and efficiency. Numerical study of the DLR-F4 wing–body combination with a mending plate patched on the wing upper surface is carried out with the in-house code NSAWET. A sharp pressure jump and an approximate one-count drag increment brought by the plate can be captured.
In this paper the principles of the FOAM C++ class library for continuum mechanics are outlined. The intention is to make it as easy as possible to develop reliable and efficient computational continuum mechanics (CCM) codes: this is achieved by making the top level syntax of the code as close as possible to conventional mathematical notation for tensors and partial differential equations. Object orientation techniques enable the creation of data types which closely mimic those of continuum mechanics, and the operator overloading possible in C++ allows normal mathematical symbols to be used for the basic operations. As an example, the implementation of various types of turbulence modelling in a FOAM computational uid-dynamics (CFD) code is discussed, and calculations performed on a standard test case, that of flow around an square prism, are presented. To demonstrate the exibility of the FOAM library, codes for solving structures and magneto-hydrodynamics are also presented w...
An effective way of using computational fluid dynamics (CFD) to simulate flow about a rotating device—for example, a wind or marine turbine—is to embed a rotating region of cells inside a larger, stationary domain, with a sliding interface between. This paper describes a simple but effective method for implementing this as an internal Dirichlet boundary condition, with interfacial values obtained by interpolation from halo nodes. The method is tested in two finite-volume codes: one using block-structured meshes and the other unstructured meshes. Validation is performed for flow around simple, isolated, rotating shapes (cylinder, sphere and cube), comparing, where possible, with experiment and the alternative CFD approach of fixed grid with moving walls. Flow variables are shown to vary smoothly across the sliding interface. Simulations of a tidal-stream turbine, including both rotor and support, are then performed and compared with towing-tank experiments. Comparison between CFD and experiment is made for thrust and power coefficients as a function of tip-speed ratio (TSR) using Reynolds-averaged Navier–Stokes turbulence models and large-eddy simulation (LES). Performance of most models is good near the optimal TSR, but simulations underestimate mean thrust and power coefficients in off-design conditions, with the standard k– ϵ turbulence model performing noticeably worse than shear stress transport k– ω and Reynolds-stress-transport closures. LES gave good predictions of mean load coefficients and vital information about wake structures but at substantial computational cost. Grid-sensitivity studies suggest that Reynolds-averaged Navier–Stokes models give acceptable predictions of mean power and thrust coefficients on a single device using a mesh of about 4 million cells. Copyright © 2013 John Wiley & Sons, Ltd.
This paper presents an implementation of the Generalized Grid Interface (GGI) for OpenFOAM. It is used to couple multiple non-conformal regions into a single contiguous domain at matrix level. The main advantage of the Generalized Grid Interface comes from removing the requirement to adjust the topology of the mesh at the interface between two non-conformal meshes. Instead, a set of weighting factors is evaluated in order to properly balance the flux at the GGI interface. Evaluation of the GGI weighting factors is based on the precise computation of the patch faces intersection on each side of the coupling interface as follows from discretisation. This is complicated due to the different grid resolution of the mesh on each side of the interface. This paper describes the choice and implementation of robust and quick algorithms for computing the GGI weighting factors. Furthermore, for turbomachinery simulations in particular, various derived forms of GGI are used regularly. Cyclic GGI, partial GGI and mixing plane GGI are all variants of the basic GGI interface that are needed for various use cases. Finally, it is very important that the GGI interface can be used for parallel OpenFOAM simulations on clusters of computers; otherwise, this would impose a severe limit on the size of the problems. This paper will show the current state of development of the Generalized Grid Interface for turbomachinery simulations and steps towards its generalisation and parallelisation.
The premise of this paper is the observation that the engineering community in general, and the NASA aeronautics program in particular, have not been active participants in the renewed interest in high performance computing at the national level. Advocacy for high performance computing has increasingly been taken up by the science community with the argument that computational methods are becoming a third pillar of scientific discovery alongside theory and experiment. Computational engineering, on the other hand, has continually been relegated to a set of mature software tools which run on commodity hardware, with the notion that engineering problems are not complex enough to warrant the deployment of state-of-the-art hardware on such a vast scale. We argue that engineering practices can benefit equally from an aggressive program in high performance computational methods, and that these problems are at least as important as science problems, particularly with regards to any national competitiveness agenda. Because NASA aeronautics has historically been a principal driver of computational engineering research and development, the current situation represents an opportunity for the NASA aeronautics program to resume its role as a leading advocate for high performance computational engineering at the national level. We outline a sample set of Grand Challenge problems which are used to illustrate the potential benefits a reinvigorated program could produce, and use these examples to identify critical barriers to progress and required areas of investment. We conclude by noting that other communities have spent significant efforts in formulating the case for increased investment in high performance computing activities, and that a similar roadmap will be required for the engineering community. I.
Computational fluid dynamics (CFD) codes today represent consolidated tools that cover most physical and chemical processes which occur during operation of internal combustion engines under steady and unsteady conditions. Despite the availability of advanced physical models, the most demanding prerequisite for a CFD engine code is its flexibility in mesh structure and geometry handling capacity to accommodate moving boundaries. In fact, while the motion is solely defined on boundary points, most CFD approaches a-priori specify the position of every mesh vertex in the mesh for every time-step. Alternatives exist, most commonly using mesh generation techniques, like smoothing. In practice this is quite limiting, as it becomes difficult to prescribe solution-dependent motion or perform mesh motion on dynamically adapting meshes. To preserve the mesh quality during extreme boundary deformation due to piston and valve motion, the number of the cells in the mesh needs to be changed. For this reason a set of "topological changes" has been defined, allowing the possibility of attaching or detaching boundaries, adding or removing cell layers and using sliding mesh interfaces. This paper presents a new method of handling motion and topological changes in a moving-mesh Finite Volume Method (FVM). It consists of self-contained mesh topology modifiers which operate without direct "event" prescription and a vertex-based unstructured mesh motion solver. Mesh motion is determined by solving a motion equation with variable diffusion on mesh points, using a Finite Element method with polyhedral cell support. This guarantees that an initial valid mesh remains geometrically valid for arbitrary boundary motion. The proposed algorithms have been implemented in the OpenFOAM code, in order to perform mesh motion on the most common engine geometries. The proposed mesh setup relies on a static initial mesh which can be generated by standard commercial and open-source tools. The final part of the work concerns the application of the Finite Volume Method on moving meshes with topological changes, considering different test cases and preliminary results of the simulation of in-cylinder gas-exchange phase and combustion process for simplified geometries.
Launched in January 2005, VIRTUE initially concentrates on the development of new, and the improvement of existing, Computational Fluid Dynamics tools which will allow an integrated and complete numerical analysis of marine hydrodynamic behaviour in a virtual environment – the Virtual Tank Utility. Hence it will complement traditional experimental analysis. By improving the accuracy, flexibility and reliability of CFD predictions, and by integrating presently disparate tools into an integrated platform, VIRTUE will deliver important advantages to the shipbuilding industry, including reduced manufacturing costs through shorter lead times and more focussed designs; improved design and product quality and an increased range and quality of services offered by European hydrodynamics service providers.
Clipping 2D polygons is one of the basic routines in computer graphics. In rendering complex 3D images it has to be done several thousand times. Efficient algorithms are therefore very important. We present such an efficient algorithm for clipping arbitrary 2D-polygons. The algorithm can handle arbitrary closed polygons, specifically where the clip and subject polygons may self-intersect. The algoirthm is simple and faster that Vatti's (1992) algorithm, which was designed for the general case as well. Simple modifications allow determination of union and set-theoretic differences of two arbitrary polygons.
This work presents a new and efficient strategy to handle non-conformal interfaces with the aim of assuring the conservation of fluxes in Finite Volume problems. A conservative interpolation is developed for general transport equations. Due to the arbitrary connectivity between the interfaces, the interpolations require flux-based weights defining a complex numerical stencil. In this context, a new method is proposed to simplify the coupling at the interface based on the construction of a simplified supermesh. Here, a supermesh is not completely defined, instead, the interface faces are logically duplicated (or multiplied) to generate a one-to-one connectivity between them. The simplified supermesh named pseudo-supermesh eliminates the interpolations and assures the conservation of fluxes based on the trivial connectivity. The area and the geometrical centroid of the new faces are redefined according to the overlapped sector of the original faces using the local supermeshing approach. Since the arbitrary polygons resulting from the face intersections are not generated and introduced into the mesh, computational cost and implementation efforts are saved. The proposed method is tested focusing on the conservation of fluxes and on the accuracy, showing conservation to machine precision and second order convergence as expected. In order to be able to solve large problems, the methodology is designed and implemented to be run in parallel architectures showing an excellent efficiency.
In computational fluid dynamics (CFD) or computational aeroacoustics (CAA) applications, it is often necessary to exchange flow data between grid blocks with a sliding interface, where grid node connectivity does not exist. Usually, pointwise interpolation/extrapolation or overset grid is employed to pass flow data across such an interface. However, because of the non-conservative nature of these treatments, conservations of mass, momentum, and energy may not be guaranteed in the numerical solution, and thus ultimately causes errors. Another treatment in the literature is to directly employ surface fluxes in the finite volume scheme for data exchange across the interface. In the present paper, based on a cell-centered unstructured upwind scheme, a rigorous conservative treatment of the flow data across an interface with no grid connectivity or a sliding interface is proposed. The implementation is simple and the performance is demonstrated in several numerical examples. Copyright © 2009 by the American Institute of Aeronautics and Astronautics, Inc.
This paper presents a new sliding mesh technique for the computation of unsteady viscous flows in the presence of rotating bodies. The compressible Euler and incompressible Navier-Stokes equations are solved using a higher-order (> 2) finite volume method on unstructured grids. A sliding mesh approach is employed at the interface between computational grids in relative motion. In order to prevent loss of accuracy, two distinct families of higher-order sliding mesh interfaces are developed. These approaches fit naturally
in a high-order finite volume framework. To this end, Moving Least Squares (MLS) approximants are used for the transmission of the information for one grid to another. A particular attention is paid for the study of the
accuracy and conservation properties of the numerical scheme for static and rotating grids. The capabilities of the present solver to compute complex unsteady vortical flow motions created by rotating geometries are illustrated on a cross-flow configuration.
A coupling method based on the overset grid approach has been successfully developed to couple multi-copies of a massively-parallel unstructured compressible LES solver AVBP for turbomachinery applications. As proper LES predictions require minimizing artificial dissipation as well as dispersion of turbulent structures, the numerical treatment of the moving interface between stationary and rotating components has been thoroughly tested on cases involving acoustical wave propagation, vortex propagation through a translating interface and a cylinder wake through a rotating interface. Convergence and stability of the coupled schemes show that a minimum number of overlapping points are required for a given scheme. The current accuracy limitation is locally given by the interpolation scheme at the interface, but with a limited and localized error. For rotor–stator type applications, the moving interface only introduces a spurious weak tone at the rotational frequency provided the latter is correctly sampled. The approach has then been applied to the QinetiQ MT1 high-pressure transonic experimental turbine to illustrate the potential of rotor/stator LES in complex, high Reynolds-number industrial turbomachinery configurations. Both wave propagation and generation are considered. Mean LES statistics agree well with experimental data and bring improvement over previous RANS or URANS results.
The Chimera method was developed three decades ago as a meshing simplification tool. Different components are meshed independently and then glued together using a domain decomposition technique to couple the equations solved on each component. This coupling is achieved via transmission conditions (in the finite element context) or by imposing the continuity of fluxes (in the finite volume context). Historically, the method has then been used extensively to treat moving objects, as the independent meshes are free to move with respect to the others. At each time step, the main task consists in recomputing the interpolation of the transmission conditions or fluxes. This paper presents a Chimera method applied to the Navier–Stokes equations. After an introduction on the Chimera method, we describe in two different sections the two independent steps of the method: the hole cutting to create the interfaces of the subdomains and the coupling of the subdomains. Then, we present the Navier–Stokes solver considered in this work. Implementation aspects are then detailed in order to apply efficiently the method to this specific parallel Navier–Stokes solver. We conclude with some examples to demonstrate the reliability and application of the proposed method. Copyright © 2014 John Wiley & Sons, Ltd.
A polygon hidden surface and hidden line removal algorithm is presented. The algorithm recursively subdivides the image into polygon shaped windows until the depth order within the window is found. Accuracy of the input data is preserved.The approach is based on a two-dimensional polygon clipper which is sufficiently general to clip a concave polygon with holes to the borders of a concave polygon with holes.A major advantage of the algorithm is that the polygon form of the output is the same as the polygon form of the input. This allows entering previously calculated images to the system for further processing. Shadow casting may then be performed by first producing a hidden surface removed view from the vantage point of the light source and then resubmitting these tagged polygons for hidden surface removal from the position of the observer. Planar surface detail also becomes easy to represent without increasing the complexity of the hidden surface problem. Translucency is also possible.Calculation times are primarily related to the visible complexity of the final image, but can range from a linear to an exponential relationship with the number of input polygons depending on the particular environment portrayed. To avoid excessive computation time, the implementation uses a screen area subdivision preprocessor to create several windows, each containing a specified number of polygons. The hidden surface algorithm is applied to each of these windows separately. This technique avoids the difficulties of subdividing by screen area down to the screen resolution level while maintaining the advantages of the polygon area sort method.
The study of rotor–fuselage interactional aerodynamics is central to the design and performance analysis of helicopters. However, regardless of its significance, rotor–fuselage aerodynamics has so far been addressed by very few authors. This is mainly due to the difficulties associated with both experimental and computational techniques when such complex configurations, rich in flow physics, are considered. In view of the above, the objective of this study is to develop computational tools suitable for rotor–fuselage engineering analysis based on computational fluid dynamics (CFD).
To account for the relative motion between the fuselage and the rotor blades, the concept of sliding meshes is introduced. A sliding surface forms a boundary between a CFD mesh around the fuselage and a rotor-fixed CFD mesh which rotates to account for the movement of the rotor. The sliding surface allows communication between meshes. Meshes adjacent to the sliding surface do not necessarily have matching nodes or even the same number of cell faces. This poses a problem of interpolation, which should not introduce numerical artefacts in the solution and should have minimal effects on the overall solution quality. As an additional objective, the employed sliding mesh algorithms should have small CPU overhead. The sliding mesh methods developed for this work are demonstrated for both simple and complex cases with emphasis placed on the presentation of the inner workings of the developed algorithms. Copyright
The objective of this work is to develop a sliding interface method for simulations involving relative grid motion that is fast and efficient and involves no grid deformation, remeshing, or hole cutting. The method is implemented into a parallel, node-centred finite volume, unstructured viscous flow solver. The rotational motion is accomplished by rigidly rotating the subdomain representing the moving component. At the subdomain interface boundary, the faces along the interface are extruded into the adjacent subdomain to create new volume elements forming a one-cell overlap. These new volume elements are used to compute a flux across the subdomain interface. An interface flux is computed independently for each subdomain. The values of the solution variables and other quantities for the nodes created by the extrusion process are determined by linear interpolation. The extrusion is done so that the interpolation will maintain information as localized as possible. The grid on the interface surface is arbitrary. The boundary between the two subdomains is completely independent from one another; meaning that they do not have to connect in a one-to-one manner and no symmetry or pattern restrictions are placed on the grid. A variety of numerical simulations were performed on model problems and large-scale applications to examine conservation of the interface flux. Overall solution errors were found to be comparable to that for fully connected and fully conservative simulations. Excellent agreement is obtained with theoretical results and results from other solution methodologies. Copyright © 2006 John Wiley & Sons, Ltd.
Mesh adaptivity on unstructured meshes is a proven and popular tool for reducing the computational cost of numerical simulations. Unstructured meshes are often preferred in mesh adaptivity as they allow for greater geometric flexibility and arbitrary anisotropy in resolving simulation features. However, such mesh adaptivity suffers from a significant drawback: the interpolation errors caused by interpolating from the old mesh to the new mesh typically destroys conservation of quantities important to the physical accuracy of the simulation (e.g., density, volume fraction, tracer concentration, etc.). This work presents several globally conservative interpolation operators between general unstructured meshes via the construction of an intermediate supermesh. The construction of the supermesh is performed by transforming the problem to the input to a constrained meshing problem. The performance of the conservative interpolation operators are compared against interpolation using the underlying basis functions.
The problem of interpolating between discrete fields arises frequently in computational physics. The obvious approach, consistent interpolation, has several drawbacks such as suboptimality, non-conservation, and unsuitability for use with discontinuous discretisations. An alternative, Galerkin projection, remedies these deficiencies; however, its implementation has proven very challenging. This paper presents an algorithm for the local implementation of Galerkin projection of discrete fields between meshes. This algorithm extends naturally to three dimensions and is very efficient.
A new family of clipping algorithms is described. These algorithms are able to clip polygons against irregular convex plane-faced volumes in three dimensions, removing the parts of the polygon which lie outside the volume. In two dimensions the algorithms permit clipping against irregular convex windows.
Polygons to be clipped are represented as an ordered sequence of vertices without repetition of first and last, in marked contrast to representation as a collection of edges as was heretofore the common procedure. Output polygons have an identical format, with new vertices introduced in sequence to describe any newly-cut edge or edges. The algorithms easily handle the particularly difficult problem of detecting that a new vertex may be required at a corner of the clipping window.
The algorithms described achieve considerable simplicity by clipping separately against each clipping plane or window boundary. Code capable of clipping the polygon against a single boundary is reentered to clip against subsequent boundaries. Each such reentrant stage of clipping need store only two vertex values and may begin its processing as soon as the first output vertex from the preceeding stage is ready. Because the same code is reentered for clipping against subsequent boundaries, clipping against very complex window shapes is practical.
For perspective applications in three dimensions, a six-plane truncated pyramid is chosen as the clipping volume. The two additional planes parallel to the projection screen serve to limit the range of depth preserved through the projection. A perspective projection method which provides for arbitrary view angles and depth of field in spite of simple fixed clipping planes is described. This method is ideal for subsequent hidden-surface computations.
A case is made for a computational fluid dynamics (CFD) effort to predict aircraft flight characteristics, with a focus on stability and control. Problems in predicting stability and control are discussed. The state-of-the-art in CFD, as it relates to aircraft flight predictions, is reviewed. Problems affecting grid convergence studies are analyzed. The computer resources needed to address flight simulation problems are estimated. The status of critical technologies is briefly discussed.
Variations of the SIMPLE method of Patankar and Spalding have been widely used over the past decade to obtain numerical solutions to problems involving incompressible flows. The present paper shows several modifications to the method which both simplify its implementation and reduce solution costs. The performances of SIMPLE, SIMPLER, and SIMPLEC (the present method) are compared for two recirculating flow problems.The paper is addressed to readers who already have experience with SIMPLE or its variants.
PATCHED grid calculations within the framework of an implicit, flux vector split upwind/relaxation algorithm for the Euler equations are presented. Aspects of computing on patched grids are discussed including the effect of a metricdiscontinuous interface on the convergence rate of the algorithm, and the effect of curvature along an interface. Applications to a converging-diverging nozzle including effects of choking and bypass slots in two dimensions are presented. © 1991 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.
An accurate numerical analysis of the flows associated with rotor-stator configurations in turbomachinery can be very helpful in optimizing the performance of turbomachinery. In this study the unsteady, thin-layer, Navier-Stokes equations are solved using a system of patched and overlaid grids for a rotor-stator configuration of an axial turbine. The equations necessary for an accurate transfer of information between the several grids are briefly described within the framework of an iterative, implicit algorithm. Results in the form of Mach number contours, time-averaged pressures, unsteady pressures, amplitudes, and phase are presented. The numerical results are also compared with experimental data and the agreement is found to be good.
Patched grid calculations within the framework of an implicit, flux-vector split upwind/relaxation algorithm for the Euler equations are presented. The effect of a metric-discontinuous interface on the convergence rate of the algorithm is discussed along with the spatial accuracy of the solution and the effect of curvature along an interface. Results are presented and discussed for the free-stream problem, shock reflection problem, supersonic inlet with a 5 degree ramp, aerodynamically choked inlet, and three-dimensional analytic forebody.
CFD Vision 2030 Study: A Path to Revolutionary Computational Aerosciences, Mchenry County Natural Hazards Mitigation Plan
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Automatic mesh motion with topological changes for engine simulation
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T. Lucchini, G. D'Errico, H. Jasak, Z. Tukovic, Automatic mesh motion with topological changes for engine simulation, Tech. Rep., SAE Technical Paper
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A compressible dynamic solver for the simulation of turbulent flows in IC engine geometries, International Multidimensional Engine Modeling User's Group Meeting At the SAE Congress
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An overset grid method for large eddy simulation of turbomachinery stages
- G Wang
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G. Wang, F. Duchaine, D. Papadogiannis, et al., An overset grid method for large eddy simulation of turbomachinery stages, J. Comput. Phys 274 (2014)
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Galerkin projection of discrete fields via supermesh construction Ph
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P.E. Farrell, Galerkin projection of discrete fields via supermesh construction Ph.D. Thesis, Imperial College London, 2009.
A compressible dynamic solver for the simulation of turbulent flows in IC engine geometries
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