龙格库塔间断有限元方法在计算爆轰问题中的应用

Runge-Kutta Discontinuous Galerkin Method for Detonation Waves

构造求解带源项守恒律方程组的龙格库塔间断有限元(RKDG)方法,并分别结合源项的Strang分裂法和无分裂法数值求解模型守恒律方程和反应欧拉方程.为了和有限体积型WENO方法进行比较,设计计算源项的WENO重构格式.对一维带源项守恒律的计算表明,对于非刚性问题,RKDG方法比有限体积型WENO方法的误差更小;对于刚性问题,RKDG方法对于间断面位置的捕捉更为精确.对于一二维爆轰波问题的计算结果表明,RKDG方法对爆轰波结构的分辨和爆轰波位置的捕捉能力更强.

A Runge-Kutta discontinuous Galerkin（RKDG） method for conservation law with source term is shown.The method is implemented with Strang split or unsplit methods,and is applied to solve one-dimensional conservation law with source term as well as one and two-dimensional detonation wave problems.In order to compare with the fifth-order finite volume WENO method,a special reconstruction method is proposd to calculate integration of the source term with high-order spatial accuracy.Numerical tests in one dimension show that the RKDG method has smaller errors than WENO method for nonstiff problems and is more accurate in capturing position of discontinuity in stiff problems.Numerical simulations of detonation waves demonstrate that the RKDG method is more effcient in resolving detailed structure of detonation waves and location of detonation front.