2类高阶格式数值测试和比较

Numerical Study of Two High-Order Schemes for Compressible Euler Equation

通过求解二维Burgers方程初边值问题、二维周期漩涡问题、Richtmyer Meshkov(简称RM)不稳定性问题和Ray-leigh-Taylor(简称RT)不稳定性问题,对五阶FD-WENO格式(简称WENO5)及二阶Godunov格式MUSCL进行了数值测试和比较.所得结果对于求解气体动力学问题及辐射流体力学问题时,怎样恰当地选择数值方法具有一定参考作用.

A numerical study is undertaken to compare the fifth-order finite difference weighted essentially non-oscillatory scheme （FD-WEN05） to the second-order Godunov scheme MUSCL （monotonic upstream-centered scheme for conservation laws）. For quantitative comparison purpose, these methods are tested on a series of problems whose true solutions are known or can be computed with high accuracy, such as the two-dimensional Burgers initial problems, the two-dimensional periodic vortex problem, Richtmyer-Meshkov instability problems and Rayleigh-Taylor instability problems. The results can be referred to as to how to choose the numerical method when solving the problems of gas dynamics and radiation hydrodynamics.