Advances in Numerical Magnetohydrodynamics -- Novel Schemes and Adaptive Mesh Refinement on Structured Meshes

DMS Award AbstractAward #： 0204640 PI： Balsara，Dinshaw机构： 圣母大学课程： 计算数学程序经理：凯瑟琳Mavriplis标题：在数值磁流体力学的进展-新的计划和自适应网格细化结构网格最近的文献已经看到了爆炸的兴趣在数值磁流体力学（MHD）领域。这源于这样一个事实，即强大的总变差递减（TVD）计划已制定和自适应网格细化（AMR）技术已被设计。MHD方程以无发散的方式演化磁场，这种无发散的演化对于MHD系统的物理一致性计算至关重要。理想的MHD格式具有二阶精度。在这个项目中，我们专注于AMR网格上电阻MHD的二阶精度方法的制定。这项工作将依赖于Krylov子空间技术的使用。电阻磁流体力学方程在物理学、天体物理学和工程学的各种设置中使用。它们对火箭推进的先进方法以及核聚变发电很有用。因此，能够理解如何解决这些方程将有助于社会，因为它将帮助我们在那些非常有用的应用上取得进展。在这些社会上有用的应用程序中，兴趣往往集中在解决这些问题的自适应网格，以有效地解决方案。因此，我们将集中精力制定二阶精度技术的电阻自适应网格细化磁流体力学在这项工作中。

DMS Award AbstractAward #: 0204640PI: Balsara, DinshawInstitution: University of Notre DameProgram: Computational MathematicsProgram Manager: Catherine MavriplisTitle: Advances in Numerical Magnetohydrodynamics - Novel Schemes and Adaptive Mesh Refinement on Structured Meshes The recent literature has seen an explosion of interest in the field of numerical magnetohydrodynamics (MHD). This stems from the fact that robust total variation diminishing (TVD) schemes have been formulated and adaptive mesh refinement (AMR) techniques have been designed. The MHD equations evolve the magnetic field in divergence-free fashion and this divergence-free evolution is essential for physically consistent computation of the MHD system. The ideal MHD schemes that have been formulated have second order accuracy. In this project we focus on the formulation of second order accurate methods for resistive MHD on AMR meshes. The work will rely on the use of Krylov subspace techniques.The equations of resistive magnetohydrodynamics are used in various settings in physics, astrophysics and engineering. They are useful for advanced methods for rocket propulsion as well as in nuclear fusion-based power generation. As a result, being able to understand how to solve these equations will help society because it will help us make progress on those very useful applications. In several of these societally useful applications, interest often focuses on solving these problems on an adaptive mesh in order to efficiently resolve solutions. As a result, we will focus on formulating second order accurate techniques for resistive adaptive mesh refinement magnetohydrodynamics in this work.Date: June 24, 2002