Multigrid Strategies for CFD Problems on Non-Structured Meshes
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Multigrid method
Computational fluid dynamics (CFD) has been proven to be a versatile tool for indoor environment simulations. The discretization of computational domain (mesh generation) determines the reliability of CFD simulation and computational cost. For cases with complex/irregular geometries, the widely utilized tetrahedral meshes have critical limitations, including low accuracy, considerate grid number and computing cost. To overcome these disadvantages, the current research developed a polyhedral meshes based meshing strategy for indoor environment simulations. This study applied tetrahedral, hexahedral and polyhedral meshes for evaluating indoor environment cases developed from previous studies. Simulation accuracy, computing time and physical storage of different mesh types were compared. The results show that the polyhedral meshes could save almost 95% of computing time without sacrificing model accuracy, compared with the other two mesh types with the approximately same grid numbers. Due to its large mesh information, the polyhedral meshes occupied the most physical memory. Overall, the polyhedral meshes based meshing strategy produced a superior performance (model accuracy and computing time) for indoor environment simulations and shows a great potential in engineering applications.
Hexahedron
Volume mesh
Tetrahedron
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Multigrid method
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A new method based on a hydrid finite volume / finite element discretization of the radiative transfer equation is described and applied to multidimensional rectangular enclosures with grey absorbing-emitting-scattering media. The spatial discretization is carried out using the finite volume method and the angular discretization is performed using basis functions commonly employed in the finite element method. The predicted results for two and three-dimensional enclosures are compared with analytical solutions and show that the numerical solution converges to the analytical one as the discretization is refined.
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Abstract The simulation of engineering problems require more and more sophisticated numerical models, and finer and finer meshes discretising complex geometries. Even with the most powerful computers, these tasks are very challenging ; cheaper computing techniques are needed.
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A multigrid algorithm has been developed for solving the steady-state Euler equations in two dimensions on unstructured triangular meshes. The method assumes the various coarse and fine grids of the multigrid sequence to be independent of one another, thus decoupling the grid generation procedure from the multigrid algorithm. The transfer of variables between the various meshes employs a tree-search algorithm which rapidly identifies regions of overlap between coarse and fine grid cells. Finer meshes are obtained either by regenerating new globally refined meshes, or by adaptively refining the previous coarser mesh. For both cases, the observed convergence rates are comparable to those obtained with structured multigrid Euler solvers. The adaptively generated meshes are shown to produce solutions of higher accuracy with fewer mesh points.
Multigrid method
Volume mesh
Decoupling (probability)
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Graphics processor units (GPUs) have started becoming an integral part of high performance computing. We develop a GPU based 3D-unstructured geometric multigrid solver, which is extensively used in Computational Fluid Dynamics (CFD) applications. Parallelization for GPUs is not straightforward because of the irregularity of the mesh. Using combination of graph coloring and greedy maximal independent set computations, we obtain significant performance improvements in the multigrid solver and its parallelization. We use NVIDIAs CUDA programming model for the implementation. In our experiments, we solve heat conduction problems on unstructured 3D meshes. Different schemes for implementing the multigrid algorithm are evaluated. For a mesh of size 1.6 million, our multigrid GPU implementation gives 24 times speed up compared to multigrid serial implementation and 1630 times speed up compared to non-multigrid serial implementation.
Multigrid method
Solver
Graphics processing unit
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Volume mesh
Unstructured data
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Abstract In this paper, we consider finite volume multigrid methods on triangular meshes with control volume based intergrid transfer operators. We review the error analysis of the finite volume methods and the convergence analysis on the multigrid method. For several different triangulations, we investigate the error reduction factors of the multigrid method as a solver, and also as a preconditioner in the Preconditioned CGM and GMRES solvers. We also study the scaling properties of the finite volume multigrid method on a High Performance Computer. We identify that the intergrid transfer operator based on the trial function space has the best properties.
Multigrid method
Transfer operator
Solver
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In 3D geodynamics numerical simulation research, it is often required to mesh the whole Earth or part of the spherical shell, and the size of mesh is much more important to our research. Computing meshes not only meets the need of the geophysical analysis, but also avoids the computing redundancy caused by too small meshes near the core. In this paper, one structured refining meshing scheme is presented for Earth, which can make all mesh sizes in the Earth more uniform, and refine the meshes near the surface area so as to meet the need of the geophysical analysis. And in the simple computing trial for the earth meshes generated by the mesh scheme in this paper, good results are obtained.
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Some methods in approximation of fluxes between adjacent cells have been proposed in context of the finite volume technique on unstructured meshes. A shallow water model has been developed for testing the proposed methods. The third order Adams-Bashforth scheme is used in integrating the governing equations. A filter has been designed to remove spurious waves. The model is tested on unstructured triangular meshes with some examples in literature.
Spurious relationship
Unstructured grid
Volume mesh
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