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

University Of Notre Dame, Notre Dame IN

Investigators

Abstract

DMS Award Abstract Award #: 0204640 PI: Balsara, Dinshaw Institution: University of Notre Dame Program: Computational Mathematics Program Manager: Catherine Mavriplis Title: 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