Positivity-preserving high order finite volume hybrid Hermite WENO schemes for compressible Navier-Stokes equations
Positivity-preserving high order finite volume hybrid Hermite WENO schemes for compressible Navier-Stokes equations
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DOI：
10.1016/j.jcp.2021.110596
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
Chuan Fan;Xiangxiong Zhang;J. Qiu
中科院分区：
文献类型：
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作者：
Chuan Fan;Xiangxiong Zhang;J. Qiu
在本文中，我们通过结合非线性通量和保正限制器，为可压缩纳维-斯托克斯方程构建了保正高阶精确有限体积混合埃尔米特加权本质非振荡（HWENO）格式。 HWENO 方案比 WENO 方案具有更紧凑的模板，但由于辅助变量而具有更高的计算成本。混合 HWENO 方案在平滑区域使用线性重建，因此比传统的 HWENO 方案更有效。然而，混合 HWENO 对于许多苛刻的问题来说并不稳健。对于可压缩欧拉方程和可压缩纳维-斯托克斯方程，本文的保正性混合 HWENO 格式不仅比传统的 HWENO 方法更高效，而且鲁棒性更强，特别是对于求解低密度和低压状态下的气体动力学方程。对低密度和低压问题进行数值测试，以证明保正混合 HWENO 方案的鲁棒性和效率。
In this paper, we construct a positivity-preserving high order accurate finite volume hybrid Hermite Weighted Essentially Non-oscillatory (HWENO) scheme for compressible Navier-Stokes equations, by incorporating a nonlinear flux and a positivity-preserving limiter. HWENO schemes have more compact stencils than WENO schemes but with higher computational cost due to the auxiliary variables. The hybrid HWENO schemes use linear reconstructions in smooth region thus are more efficient than conventional HWENO schemes. However, the hybrid HWENO is not robust for many demanding problems. The positivity-preserving hybrid HWENO scheme in this paper is not only more efficient but also much more robust than the conventional HWENO method for both compressible Euler and compressible Navier-Stokes equations, especially for solving gas dynamics equations in low density and low pressure regime. Numerical tests on low density and low pressure problems are performed to demonstrate the robustness and the efficiency of the positivity-preserving hybrid HWENO scheme.