Discrete velocity scheme for solving the Boltzmann equation with the GPGPU

Malkov, E. A.; Poleshkin, S. O.; Иванов, М. С.

doi:10.1063/1.4769532

Cited by 6 publications

(5 citation statements)

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“…29 For many problems, the computational times for the collision and advection parts of the Boltzmann solver were of the same order and it was necessary to develop both advection and collision CUDA kernels for GPU computing. In many other methods, implemented on GPU 32,33 , the time for the collision integral computations was much larger than for the advection, so it was not necessary to construct an effective advection scheme.…”

Section: Boltzmann Solvermentioning

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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Section: Boltzmann Solvermentioning

confidence: 99%

Adaptive kinetic-fluid solvers for heterogeneous computing architectures

Zabelok

Arslanbekov

Kolobov

2015

Journal of Computational Physics

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Section: Introductionmentioning

confidence: 99%

“…Moreover, the author establishes analytical expressions for components of the kernel of the collision integral in the case of hard spheres potential, e.g., [11,13]. Other examples of solutions of the Boltzmann equations include [14,15,16] and most recently [17,18,19,20,21,22].In [23,24] it was shown that high order DG approximations in velocity space can be very accurate in preserving mass, momentum and energy in the discrete solution even if the solution is rough. In addition, DG methods are well suited for adaptive techniques and parallel implementation.…”

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confidence: 99%

Deterministic solution of the spatially homogeneous Boltzmann equation using discontinuous Galerkin discretizations in the velocity space

Alekseenko

Josyula

2014

Journal of Computational Physics

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We present a new deterministic approach for the solution of the Boltzmann kinetic equation based on nodal discontinuous Galerkin (DG) discretizations in velocity space. In the new approach the collision operator has the form of a bilinear operator with pre-computed kernel; its evaluation requires O(n 5 ) operations at every point of the phase space where n is the number of degrees of freedom in one velocity dimension. The method is generalized to any molecular potential. Results of numerical simulations are presented for the problem of spatially homogeneous relaxation for the hard spheres potential. Comparison with the method of Direct Simulation Monte Carlo (DSMC) showed excellent agreement.

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“…In the paper [12] it has been shown how GPU computations can be used to effectively solve the relaxation problem, 40 times speedup was achieved using the deterministic method with piecewise approximation of the velocity distribution function and analytical integration over collision impact parameters. For 1D physical space a shock wave structure problem solved with another deterministic method GPU implementation demonstrated about 500 times speedup over CPU version [13].…”

Section: Introductionmentioning

confidence: 99%

Deterministic GPU Boltzmann solver

Zabelok¹,

Stroganov²,

Аристов³

2014

AIP Conference Proceedings

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A variant of discrete velocity approach for solving the Boltzmann kinetic equation with regular (deterministic) approximation of collision integrals is used in parallel implementation with NVIDIA GPU computing. Some problems, namely a uniform relaxation, nonuniform relaxation in 2D physical space are solved. Speed up of GPU Boltzmann solver is of the order 100 or more times over CPU version of the solver.

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Discrete velocity scheme for solving the Boltzmann equation with the GPGPU

Cited by 6 publications

References 0 publications

Adaptive kinetic-fluid solvers for heterogeneous computing architectures

Adaptive kinetic-fluid solvers for heterogeneous computing architectures

Deterministic solution of the spatially homogeneous Boltzmann equation using discontinuous Galerkin discretizations in the velocity space

Deterministic GPU Boltzmann solver

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