A tree-based adaptive scheme for solution of the equations of gas dynamics and magnetohydrodynamics

Abstract

A solution-adaptive scheme for solving the partial differential equations governing gas dynamics and magnetohydrodynamics is presented. The scheme makes use of a hierarchically structured mesh, in which the cells of the mesh are stored in a quadtree data structure. The scheme is based on a positive linear reconstruction method coupled with an upwind-biased flux function and a multi-stage time-stepping scheme. The upwind flux function for gas dynamics is presented briefly, and the corresponding flux function for the equations governing ideal magnetohydrodynamics is formulated and discussed. Results are presented for problems in gas dynamics and magnetohydrodynamics.