论文标题
解决质量保护错误的问题和碳纤维形成的连接问题
Addressing the issue of mass conservation error and the connected problem of Carbuncle formation
论文作者
论文摘要
我们研究质量保护误差（动量密度尖峰）和可压缩欧拉方程数值解的冲击后振荡现象。这些现象及其原因已在文献中报道[34，1]。在本文中，首先，我们比较了使用不同数值方法（有限量，与WENO和DG的有限差异和简单的WENO限制器）和Upwux Flux函数（ROE，AUSM+-UP等）相比，使用单次震动，使用单次震动，使用单次震动，使用单次震动。接下来，将质量保护误差定量用于使用一维，准二维和二维Euler方程建模的固定冲击。结果表明，使用多个固定网格的细分网格或精炼网格在冲击附近，导致减轻质量保护误差。使用使用准二维Euler方程建模的可变区域管道的流动问题来证明这一点。显示了质量保护误差与肌无力的形成之间的联系，并表明可以使用多个填充网格固化Carbuncle的初步结果。
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.
