解决质量守恒误差问题和相关的Carbuncle形成问题
Addressing the issue of mass conservation error and the connected problem of Carbuncle formation
摘要：
本文研究了可压缩欧拉方程数值解中的质量守恒误差（动量密度尖峰）及与之相关的激波后振荡现象。这些现象及其原因已在文献中报道[34，1]。在本文中，首先，我们比较了质量守恒和激波后振荡的误差，使用不同的数值方法（有限体积，有限差分与WENO和DG与简单的WENO限制器）和迎风通量函数（ROE，AUSM+-up，和其他）的组合，移动的冲击，使用一维欧拉方程建模。其次，质量守恒误差被量化为使用一维，准一维和二维欧拉方程建模的静止冲击。结果表明，使用细网格或细化网格附近的冲击，使用多个过设置网格导致减轻质量守恒误差。这是证明使用的问题，通过一个可变面积的管道建模使用准一维欧拉方程。质量守恒误差和痈形成之间的联系，初步结果表明，可以治愈的痈使用多个重叠网格也显示。
英文摘要：
We study mass conservation errors (momentum density spike) and the related phenomenon of post shock oscillations in numerical solutions of compressible Euler equations. These phenomena and their causes have been reported in literature [34, 1]. In this paper, first, we compare the mass conservation and post shock oscillation errors obtained using combinations of different numerical methods (Finite Volume, Finite Difference with WENO and DG with simple WENO limiter) and upwind flux functions (ROE, AUSM+-up, and others) for moving shocks, modelled using one-dimensional Euler equations. Next, the mass conservation error is quantified for stationary shocks modelled using one-dimensional, quasi-one-dimensional and two-dimensional Euler equations. It is shown that using a fine mesh or refining mesh near shocks using multiple over set meshes lead to mitigation of the mass conservation error. This is demonstrated using the problem of flow through a variable area duct modelled using quasi-one-dimensional Euler equations. The link between mass conservation error and carbuncle formation is shown and preliminary results indicating that the carbuncle can be cured using multiple overset meshes are also shown.
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