Solving Boltzmann equation on GPU

Kloss, Yu. Yu.; Shuvalov, P. V.; Tcheremissine, F. G.

doi:10.1016/j.procs.2010.04.120

Cited by 30 publications

(18 citation statements)

References 12 publications

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“…Direct deterministic methods of solving the Boltzmann equation include discrete velocity methods (DVM) [2][3][4][5][6][7][8][9][10][11] and spectral methods (see, e.g., [12]). Application of deterministic methods in practice is not very popular because such a solution is computationally expensive, especially for strongly non-equilibrium flows, such as flows with strong shock waves.…”

Section: Introductionmentioning

confidence: 99%

“…As the performance of computational systems has noticeably increased and computer hardware has become significantly cheaper [which is partly due to the development of graphics processing units (GPUs)], it is now becoming possible to apply deterministic methods to a wider range of rarefied flows, such as flows with a significant degree of thermal non-equilibrium. This fact spurred the development of high-performance codes for computing rarefied gas flows on the basis of the deterministic numerical solution of the Boltzmann equation [6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

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High-accuracy deterministic solution of the Boltzmann equation for the shock wave structure

et al. 2015

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A new deterministic method of solving the Boltzmann equation has been proposed. The method has been employed in numerical studies of the plane shock wave structure in a hard sphere gas. Results for Mach numbers M = 4 and M = 8 have been compared with predictions of the direct simulation Monte Carlo (DSMC) method, which has been used to obtain the reference solution. Particular attention in estimating the solution accuracy has been paid to a fine structural effect: the presence of a total temperature peak exceeding the temperature value further downstream. The results of solving the Boltzmann equation for the shock wave structure are in excellent agreement with the DSMC predictions.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

High-accuracy deterministic solution of the Boltzmann equation for the shock wave structure

et al. 2015

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“…Impressive acceleration and excellent multi-GPU scaling have been demonstrated by several groups using particle 25,26 and grid-based methods with structured meshes. 27,28 We have recently demonstrated double digit speedups on a single GPU 29 and good multi-GPU scaling for the DVM Boltzmann solver, the DSMC module, and the LBM solver, all using adaptive Cartesian meshes. 18 Coupled Vlasov and two-fluid code has been recently described using GPU for Vlasov solvers in locally selected kinetic domains.…”

Section: Challenges Of Porting Adaptive Kinetic-fluid Codes To Cpu-gpmentioning

confidence: 99%

Adaptive kinetic-fluid solvers for heterogeneous computing architectures

Zabelok

Arslanbekov

Kolobov

2015

Journal of Computational Physics

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Abstract. We show feasibility and benefits of porting an adaptive multi-scale kinetic-fluid code to CPU-GPU systems. Challenges are due to the irregular data access for adaptive Cartesian mesh, vast difference of computational cost between kinetic and fluid cells, and desire to evenly load all CPUs and GPUs. Our Unified Flow Solver (UFS) combines Adaptive Mesh Refinement (AMR) with automatic cell-by-cell selection of kinetic or fluid solvers based on continuum breakdown criteria. Using GPUs enables hybrid simulations of mixed rarefied-continuum flows with a million of Boltzmann cells with 24x24x24 velocity mesh. We describe the implementation of CUDA kernels for three modules in UFS: the direct Boltzmann solver using discrete velocity method, the Direct Simulation Monte Carlo (DSMC) solver, and a mesoscopic solver based on Lattice Boltzmann Method, all using octree Cartesian mesh. Double digit speedups on single GPU and good scaling for multiGPUs have been demonstrated.

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“…This GPU technology has been progressed by some pioneering researchers and organizations for the general purpose [8] of scientific and engineering computations. Indeed, numerous achievements have shown a dramatic acceleration of computations from CUDA on GPU, such as linear algebra [9][10][11], image processing [12], computational fluid dynamics [13][14][15], molecular dynamics [16,17] and signal processing. At present, more and more numerical methods are considered to be improved by employing the new parallel power of GPU, which foretells the promising future of GPU.…”

mentioning

confidence: 99%

Implementation of the moving particle semi-implicit method on GPU

Zhu

Cheng

Lü

et al. 2011

Sci. China Phys. Mech. Astron.

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The Moving Particle Semi-implicit (MPS) method performs well in simulating violent free surface flow and hence becomes popular in the area of fluid flow simulation. However, the implementations of searching neighbouring particles and solving the large sparse matrix equations (Poisson-type equation) are very time-consuming. In order to utilize the tremendous power of parallel computation of Graphics Processing Units (GPU), this study has developed a GPU-based MPS model employing the Compute Unified Device Architecture (CUDA) on NVIDIA GTX 280. The efficient neighbourhood particle searching is done through an indirect method and the Poisson-type pressure equation is solved by the Bi-Conjugate Gradient (BiCG) method. Four different optimization levels for the present general parallel GPU-based MPS model are demonstrated. In addition, the elaborate optimization of GPU code is also discussed. A benchmark problem of dam-breaking flow is simulated using both codes of the present GPU-based MPS and the original CPU-based MPS. The comparisons between them show that the GPU-based MPS model outperforms 26 times the traditional CPU model. moving particle semi-implicit method (MPS), graphics processing units (GPU), compute unified device architecture (CUDA), neighbouring particle searching, free surface flow PACS: 47.10.ad, 45.10Db In the community of Computational Fluid Dynamics, many mesh-based methods have been developed so far to solve various problems of fluid flows. However, the well developed numerical methods such as the finite difference (volume) method, finite element method and boundary element method remain great challenges in dealing with the violent free surface flow with large deformation. Meshless methods were developed to overcome the inherent difficulties in the numerical methods based on mesh generation. Firstly, Monaghan [1] proposed the Smoothed Particle Hydrodynamics (SPH) method to deal with the astrophysical hydrodynamic problems. In SPH, the kernel approximations are used to interpolate the unknowns using particles in the Lagrangian sense. Later, this method was extended to computational fluid dynamics. Monaghan [2] and Shao [3] improved the original SPH to simulate the incompressible Newtonian fluid flows with a free surface. In addition, Koshizuka [4] proposed another particle-based method called Moving Particle Semi-implicit (MPS) for the incompressible viscous fluid flow. By MPS, the fluid flow is represented by moving particles and the convection term is calculated by the motion of these moving particles. Even if the fragmentation or merging of fluid occurs, the interfaces can be represented clearly. MPS method has been used successfully in solving many problems, such as the breaking waves [5], water sloshing [6] and tracking the free surface [7]. However, just as other particle-based CFD methods, MPS is shown to be very time-consuming, mainly because of the required searching procedure for the neighbouring

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Solving Boltzmann equation on GPU

Cited by 30 publications

References 12 publications

High-accuracy deterministic solution of the Boltzmann equation for the shock wave structure

High-accuracy deterministic solution of the Boltzmann equation for the shock wave structure

Adaptive kinetic-fluid solvers for heterogeneous computing architectures

Implementation of the moving particle semi-implicit method on GPU

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