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

奖项编号：0204640PI: Balsara， dinsha机构：圣母大学项目：计算数学项目经理：Catherine mavriplis标题：数值磁流体动力学进展-结构网格的新方案和自适应网格细化最近的文献已经看到了数值磁流体动力学（MHD）领域的兴趣爆炸。这源于稳健的总变差递减（TVD）方案的制定和自适应网格细化（AMR）技术的设计。MHD方程以无散度的方式演化磁场，这种无散度的演化对于MHD系统的物理一致性计算是必不可少的。所制定的理想MHD格式具有二阶精度。在本项目中，我们重点研究了AMR网格上电阻MHD的二阶精确方法的制定。这项工作将依赖于克雷洛夫子空间技术的使用。电阻磁流体动力学方程在物理学、天体物理学和工程学的各种场合中都有应用。它们对火箭推进的先进方法以及基于核聚变的发电都很有用。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这些非常有用的应用上取得进展。在这些对社会有用的应用中，人们的兴趣往往集中在自适应网格上解决这些问题，以便有效地解决问题。因此，在这项工作中，我们将专注于制定二阶精确的电阻自适应网格细化磁流体动力学技术。日期：2002年6月24日

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