Van Leer Advection Algorithm in the MACH2 Computer Code.

摘要

The van Leer advection algorithm has been added to the two dimensional magnetohydrodynamics code, MACH2. The mathematical theory and the implementation for nonmagnetic quantities are discussed. One dimensional test problems are presented to compare this algorithm with the Godunov advection algorithm, which was previously used in MACH2. The new implementation induces less smoothing on advected discontinuities, while maintaining the monotonic property of cell-centered distributions. A special treatment of the momentum advection is required to maintain a monotonic velocity distribution. The net practical result is a substantial savings on computational time as the van Leer algorithm requires less resolution to achieve the same level of convergence as the Godunov algorithm for dynamic problems.