Development of a modified Runge-Kutta scheme with TVD limiters for the ideal 1-D MHD equations

摘要

A fourth-order modified Range-Kutta scheme augmented with TVD models have been developed to solve the 1D MHD equations. ^The numerical scheme is applied to the benchmark magnetic shock tube problem. ^Several limiters for each TVD model have been extensively investigated, and the solutions are compared to each other and analytical solutions when available. ^The numerical scheme is proven to be accurate with ability to capture strong shocks, thin contact surfaces, and other physical phenomena occurring in the flowfield without any or with minimum oscillations in the solution. ^(Author)