This paper concerns the development of high-order multidimensional gas kinetic schemes for the Navier-Stokes solutions.In the current approach,the state-of-the-art WENO-type initial reconstruction and the gas-kinetic ...This paper concerns the development of high-order multidimensional gas kinetic schemes for the Navier-Stokes solutions.In the current approach,the state-of-the-art WENO-type initial reconstruction and the gas-kinetic evolution model are used in the construction of the scheme.In order to distinguish the physical and numerical requirements to recover a physical solution in a discretized space,two particle collision times will be used in the current high-order gas-kinetic scheme(GKS).Different from the low order gas dynamic model of the Riemann solution in the Godunov type schemes,the current method is based on a high-order multidimensional gas evolution model,where the space and time variation of a gas distribution function along a cell interface from an initial piecewise discontinuous polynomial is fully used in the flux evaluation.The high-order flux function becomes a unification of the upwind and central difference schemes.The current study demonstrates that both the high-order initial reconstruction and high-order gas evolution model are important in the design of a high-order numerical scheme.Especially,for a compact method,the use of a high-order local evolution solution in both space and time may become even more important,because a short stencil and local low order dynamic evolution model,i.e.,the Riemann solution,are contradictory,where valid mechanism for the update of additional degrees of freedom becomes limited.展开更多
基金Supported by the Natural Science Foundation of Hunan Province (12JJ6006)the Hunan Province Science and Technology Project (2012FJ3107)the National Natural Science Foundation of China (11071222)
基金supported by Hong Kong Research Grant Council(Grant No.621011)HKUST research fund(Grant No.SRFI11SC05)
文摘This paper concerns the development of high-order multidimensional gas kinetic schemes for the Navier-Stokes solutions.In the current approach,the state-of-the-art WENO-type initial reconstruction and the gas-kinetic evolution model are used in the construction of the scheme.In order to distinguish the physical and numerical requirements to recover a physical solution in a discretized space,two particle collision times will be used in the current high-order gas-kinetic scheme(GKS).Different from the low order gas dynamic model of the Riemann solution in the Godunov type schemes,the current method is based on a high-order multidimensional gas evolution model,where the space and time variation of a gas distribution function along a cell interface from an initial piecewise discontinuous polynomial is fully used in the flux evaluation.The high-order flux function becomes a unification of the upwind and central difference schemes.The current study demonstrates that both the high-order initial reconstruction and high-order gas evolution model are important in the design of a high-order numerical scheme.Especially,for a compact method,the use of a high-order local evolution solution in both space and time may become even more important,because a short stencil and local low order dynamic evolution model,i.e.,the Riemann solution,are contradictory,where valid mechanism for the update of additional degrees of freedom becomes limited.
