High Resolution Finite Volume Scheme Based on the Quintic Spline Reconstruction on Non-uniform Grids

被引:1
|
作者
Huang, Wen-Feng [1 ,2 ]
Ren, Yu-Xin [1 ]
Wang, Qiuju [3 ]
Jiang, Xiong [2 ]
机构
[1] Tsinghua Univ, Beijing 100084, Peoples R China
[2] China Aerodynam Res & Dev Ctr, Mianyang 621000, Peoples R China
[3] Inst Appl Phys & Computat Math, Beijing 100094, Peoples R China
关键词
Quintic spline reconstruction; Finite volume method; Non-uniform grids; Curvilinear coordinates; Hybrid scheme; SHOCK-TURBULENCE INTERACTION; NAVIER-STOKES EQUATIONS; DIFFERENCE-SCHEMES; NUMERICAL-SIMULATION; COMPRESSIBLE FLOWS; CONSERVATION-LAWS; RIEMANN SOLVERS; WENO SCHEME; INTERPOLATION; MESHES;
D O I
10.1007/s10915-017-0524-6
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This paper presents a compact quintic spline reconstruction for finite volume method on non-uniform structured grids. The primitive function of a dependent variable is reconstructed by a piece-wise quintic polynomial by requiring the derivatives up to fourth order being continuous at the cell interfaces. This procedure results in a block tridiagonal system of linear equations which can be solved efficiently by incorporating certain boundary closure relations. There are some distinct features in the quintic spline reconstruction. Firstly, the reconstruction stencil is compact; Secondly, the reconstruction can be applied on arbitrary non-uniform grids; and finally, the reconstruction is continuous at cell interface without the need of a Riemann solver. To stabilize the scheme, the sixth order artificial viscosity is introduced. The quintic spline reconstruction achieves sixth-order accuracy on uniform grids without artificial viscosity and fifth-order accuracy on both uniform and non-uniform grids when artificial viscosity is added. The splined scheme is blended with shock-capturing WENO scheme to suppress non-physical oscillations near discontinuities. Numerical results demonstrate the accuracy, robustness and efficiency of the proposed scheme.
引用
收藏
页码:1816 / 1852
页数:37
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