一种基于高阶节点间断Galerkin方法的新型限制器设计

A Novelly Designed Limiter for Nodal Discontinuous Galerkin Method with High-Order Accuracy

使用高阶间断Galerkin(discontinuous Galerkin,DG)方法求解双曲守恒律方程组时,非物理效应常常导致计算过程的中断,这在很大程度上制约着该方法在计算流体力学中的应用.文章结合局部单元上原始流动变量的Taylor展开,设计了一种新型的限制器,通过对各阶空间导数的重构,有效地消除了非物理振荡的不利影响.对二维Euler方程的计算结果表明,该限制器不仅能够捕捉高质量的激波,而且能够保证残值的有效收敛.

As hyperbolic conservation equations were solved by the discontinuous Galerkin（DG） method,non-physical effection usually took place and brought about the interruption of computing procedure,which restricted the application in CFD. Based on the Taylor expansion for the original physical variables on local elements,a novel limiter was designed by reconstruction of special derivative,which was used to eliminate the disadvantage of non-physical oscillation. The numerical results for the 2D Euler equation show that not only the shock wave location can be captured exactly but also an effective convergence rate can be achieved by this limiter.