Abstract

When solving multidimensional problems of gas dynamics, finite-volume schemes using complete (i.e., based on a three-wave configuration) solvers of the Riemann problem suffer from shock-wave instability. It can appear as oscillations that cannot be damped by slope limiters, or it can lead to a qualitatively incorrect solution (carbuncle effect). To combat instability, one can switch to incomplete solvers based on a two-wave configuration near the shock wave, or introduce artificial viscosity. The article compares these two approaches on unstructured grids in relation to the EBR-WENO scheme for approximating convective terms and the classical Galerkin method for approximating diffusion terms. It is shown that the method of introducing artificial viscosity usually makes it possible to more accurately reproduce the flow pattern behind the shock front. However, on a three-dimensional unstructured grid, it causes dips ahead of the front, the depth of which depends on the quality of the grid, which can lead to an emergency stop of the calculation. Switching to an incomplete solver in this case gives satisfactory results with a much lower sensitivity to the quality of the mesh.

中文翻译：

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在非结构化网格的基于边缘的方案中使用人工粘度

摘要

在求解气体动力学的多维问题时，使用黎曼问题的完整（即基于三波配置）求解器的有限体积方案会受到冲击波不稳定性的影响。它可能表现为无法被斜率限制器抑制的振荡，或者可能导致质量不正确的解决方案（痈肿效应）。为了对抗不稳定性​​，可以切换到基于冲击波附近的两波配置的不完全求解器，或者引入人工粘性。本文在非结构化网格上比较了这两种方法，用于逼近对流项的 EBR-WENO 方案和逼近扩散项的经典 Galerkin 方法。结果表明，引入人工粘度的方法通常可以更准确地再现激波前沿后的流动模式。然而，在三维非结构化网格上，它会导致前沿前倾，深度取决于网格的质量，这会导致计算的紧急停止。在这种情况下切换到不完整的求解器会得到令人满意的结果，但对网格质量的敏感度要低得多。