Solving Seven-Equation Model of Compressible Two-Phase Flow Using CUDA-GPU

Abstract

In this paper, a numerical method which combines a HLLC-type approximate Riemann solver with the third-order TVD Runge-Kutta method is presented for the two-pressure and two-velocity seven-equation model of compressible two-phase flow of Saurel and Abgrall. Based on the idea proposed by Abgrall that “a multiphase flow, uniform in pressure and velocity at t = 0, will remain uniform on the same variables during time evolution”, discretization schemes for the non-conservative terms and for the volume fraction evolution equation are derived in accordance with the adopted HLLC solver for the conservative terms. To attain high temporal accuracy, the third-order TVD Runge-Kutta method is implemented in conjunction with the operator splitting technique in a robust way by virtue of reordering the sequence of operators. Numerical tests against several one- and two-dimensional compressible two-fluid flow problems with high density and high pressure ratios demonstrate that the proposed method is accurate and robust. Besides, the above numerical algorithm is implemented on multi graphics processing units using CUDA. Appropriate data structure is adopted to maintain high memory bandwidth; skills like atom operator, counter and so on are used to synchronize thread blocks; overlapping domain decomposition method is applied for mission assignment. Using a single-GPU, we observe 31× speedup relative to a single-core CPU computation; linear speedup can be achieved by multi-GPU parallel computing although there might be a little decrease in single-GPU performance. abstract environment.

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