A positivity-preserving high order finite volume compact-WENO scheme for compressible Euler equations
A positivity-preserving high order finite volume compact-WENO scheme for compressible Euler equations
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DOI：
10.1016/j.jcp.2014.06.046
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发表时间：
2014-02
期刊：
影响因子：
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通讯作者：
Yan Guo;T. Xiong;Yufeng Shi
中科院分区：
文献类型：
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作者：
Yan Guo;T. Xiong;Yufeng Shi
本文提出了一个求解可压缩Euler方程的保正五阶有限体积紧致WENO格式。众所周知，守恒紧致有限体积格式具有高分辨率，而韦诺（加权基本无振荡）格式在流动间断附近基本无振荡。我们将韦诺格式的思想推广到一些经典的有限体积紧致格式[30]中，将低阶紧致格式与韦诺非线性权相结合，得到高阶有限体积紧致WENO格式。新发展的保正限制器[43]、[42]用于保持可压缩流体动力学Euler方程的正密度和内能。HLLC（Harten、Lax和带接触的货车Leer）近似黎曼解算器[37]、[4]用于获得单元界面处的数值通量。数值试验表明，该格式具有高阶精度、保正性、高分辨率和鲁棒性。
In this paper, a positivity-preserving fifth-order finite volume compact-WENO scheme is proposed for solving compressible Euler equations. As it is known, conservative compact finite volume schemes have high resolution properties while WENO (Weighted Essentially Non-Oscillatory) schemes are essentially non-oscillatory near flow discontinuities. We extend the idea of WENO schemes to some classical finite volume compact schemes [30], where lower order compact stencils are combined with WENO nonlinear weights to get a higher order finite volume compact-WENO scheme. The newly developed positivity-preserving limiter [43], [42] is used to preserve positive density and internal energy for compressible Euler equations of fluid dynamics. The HLLC (Harten, Lax, and van Leer with Contact) approximate Riemann solver [37], [4] is used to get the numerical flux at the cell interfaces. Numerical tests are presented to demonstrate the high-order accuracy, positivity-preserving, high-resolution and robustness of the proposed scheme.