Efficient High Accuracy Simulation for Euler and MHD Flow in Complex Geometries

复杂几何中欧拉和 MHD 流的高效高精度仿真

• 批准号: 27134793
• 负责人: Professor Dr. Claus-Dieter Munz
• 金额: --
• 依托单位: Institut für Aerodynamik und Gasdynamik (IAG)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2006
• 资助国家: 德国
• 起止时间: 2005-12-31 至 2015-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/27134793?language=en
• 关键词: Efficient; Accuracy; Simulation; Euler; MHD

A considerable amount of recent interest in science and engineering revolves around being able to simulate flows with a high level of accuracy. Finite volume schemes (FV-schemes) are amongst the most well-used schemes for such flow simulations. The standard FV-schemes for complex geometries especially based on unstructured grids are second order accurate. However, second order accuracy can be shown to be very inadequate, when the simulation of highly unsteady phenomena is required for long times or over long distances. The present proposal, which is a collaboration between research groups in the USA and Germany, seeks to improve this situation by employing Discontinuous Galerkin (DG) based algorithms of arbitrary accuracy in space and time. These schemes give the high order accuracy even on distorted unstructured grids. An important aspect of the first funding period is to improve the shock-capturing properties for high order DG schemes.Beside the simulation of fluid flow based on the Euler equation our interest also extends to the simulation of flows interacting with electro-magnetic phenomena. Here, additional requirements have to be fulfilled by the numerical method - the divergence-free property for the magnetic field and the charge conservation. In this proposal two strategies are being followed: a special space discretization method by the US group and a general a posteriori divergence cleaning strategy by the German group. The test problems and the applications of the methods developed cover typical shock problems in aerodynamics as well as in astrophysics and space physics. The divergence corrections will also be used in the simulation of pulsed plasma dynamic thrusters.

最近，科学和工程领域的大量兴趣都围绕着能够以高精度模拟流动。有限体积格式（FV-格式）是此类流动模拟中最常用的格式之一。对于复杂几何形状，特别是基于非结构网格的标准FV格式是二阶精度的。然而，当需要长时间或长距离模拟高度不稳定现象时，二阶精度可能非常不足。目前的建议，这是在美国和德国的研究小组之间的合作，旨在改善这种情况，采用不连续Galerkin（DG）为基础的算法的任意精度的空间和时间。这些格式即使在畸变的非结构网格上也具有较高的精度。第一个资助期的一个重要方面是改进高阶DG格式的激波捕捉性能。除了基于Euler方程的流体流动模拟之外，我们的兴趣还扩展到与电磁现象相互作用的流动模拟。在这里，额外的要求必须满足的数值方法-磁场和电荷守恒的发散自由属性。在这个建议中，两个策略被遵循：一个特殊的空间离散化方法由美国组和一般的后验发散清洗策略由德国组。所开发的方法的测试问题和应用涵盖了空气动力学以及天体物理学和空间物理学中的典型冲击问题。发散修正也将用于脉冲等离子体动态推力器的模拟。