Positivity-preserving high order finite difference WENO schemes for compressible Navier-Stokes equations
Positivity-preserving high order finite difference WENO schemes for compressible Navier-Stokes equations
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DOI：
10.1016/j.jcp.2022.111446
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发表时间：
2022-10
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
本文构造了可压缩Navier-Stokes(NS)方程的高阶加权本质无振荡(WENO)有限差分格式，该格式通过保持正性的通量分裂和保持尺度正性的限制器实现了密度和内能的正性保持。与传统的求解可压缩NS方程的WENO格式不同，本文的创新之处在于对保正对流扩散通量分裂的变量进行WENO重构。我们提出的方法的核心优势是稳健性和效率，特别适用于求解包括低密度和低压力流型在内的可压缩欧拉方程和NS方程的苛刻问题。此外，在计算量方面，与求解矩形区域上可压缩NS方程的保正高阶间断Galerkin格式和有限体积WENO格式相比，该格式更高效、更容易实现和推广到多维问题。基准测试表明，对于涉及低密度、低压和精细结构的苛刻问题，所提出的保正WENO格式具有高精度、高效率和健壮性，且不需要过多的人工粘性。
In this paper, we construct a high order weighted essentially non-oscillatory (WENO) finite difference discretization for compressible Navier-Stokes (NS) equations, which is rendered positivity-preserving of density and internal energy by a positivity-preserving flux splitting and a scaling positivity-preserving limiter. The novelty of this paper is WENO reconstruction performed on variables from a positivity-preserving convection diffusion flux splitting, which is different from conventional WENO schemes solving compressible NS equations. The core advantages of our proposed method are robustness and efficiency, which especially are suitable for solving tough demanding problems of both compressible Euler and NS equation including low density and low pressure flow regime. Moreover, in terms of computational cost, it is more efficient and easier to implement and extend to multi-dimensional problems than the positivity-preserving high order discontinuous Galerkin schemes and finite volume WENO scheme for solving compressible NS equations on rectangle domain. Benchmark tests demonstrate that the proposed positivity-preserving WENO schemes are high order accuracy, efficient and robust without excessive artificial viscosity for demanding problems involving with low density, low pressure, and fine structure.