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This paper presents a Graphics Processing Units (GPUs) acceleration method of an iterative scheme for gas-kinetic model equations. Unlike the previous GPU parallelization of explicit kinetic schemes, this work features a fast converging iterative scheme. The memory reduction techniques in this method enable full three-dimensional (3D) solution of kinetic model equations in contemporary GPUs usually with a limited memory capacity that otherwise would need terabytes of memory. The GPU algorithm is validated against the DSMC simulation of the 3D lid-driven cavity flow and the supersonic rarefied gas flow past a cube with grids size up to 0.7 trillion points in the phase space. The performance of the GPU algorithm is assessed by comparing with the corresponding parallel CPU program using Message Passing Interface (MPI). The profiling on several models of GPUs shows that the algorithm has a medium to high level of utilization of the GPUs computing and memory resources. A $190times$ speedup can be achieved on the Tesla K40 GPUs against a single core of Intel Xeon-E5-2680v3 CPU for the 3D lid-driven cavity flow.
In this paper, an efficient high-order gas-kinetic scheme (EHGKS) is proposed to solve the Euler equations for compressible flows. We re-investigate the underlying mechanism of the high-order gas-kinetic scheme (HGKS) and find a new strategy to impro
This paper extends the gas-kinetic scheme for one-dimensional inviscid shallow water equations (J. Comput. Phys. 178 (2002), pp. 533-562) to multidimensional gas dynamic equations under gravitational fields. Four important issues in the construction
The discrete unified gas kinetic scheme (DUGKS) is a new finite volume (FV) scheme for continuum and rarefied flows which combines the benefits of both Lattice Boltzmann Method (LBM) and unified gas kinetic scheme (UGKS). By reconstruction of gas dis
The general synthetic iteration scheme (GSIS) is extended to find the steady-state solution of nonlinear gas kinetic equation, removing the long-standing problems of slow convergence and requirement of ultra-fine grids in near-continuum flows. The ke
We demonstrate the first implementation of recently-developed fast explicit kinetic integration algorithms on modern graphics processing unit (GPU) accelerators. Taking as a generic test case a Type Ia supernova explosion with an extremely stiff ther