This paper presents a gas-kinetic theory based multidimensional high-order method for the compressible Naiver–Stokes solutions. In our previous study, a spatially and temporally dependent third-order flux scheme with the use of a third-order gas distribution function is employed. However, the third-order flux scheme is quite complicated and less robust than the second-order scheme. In order to reduce its complexity and improve its robustness, the second-order flux scheme is adopted instead in this paper, while the temporal order of method is maintained by using a two stage temporal discretization. In addition, its CPU cost is relatively lower than the previous scheme. Several test cases in two and three dimensions, containing high Mach number compressible flows and low speed high Reynolds number laminar flows, are presented to demonstrate the method capacity.
Discontinuous Galerkin Two-stage temporal discretization Gas-kinetic theory
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The current work is supported by HKUST research fund PROVOST 13SC01.
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