双曲型守恒律方程的自适应间断Galerkin方法  

Discontinuous Galerkin Adaptive Finite Element Method for Hyperbolic Conservation Law

作　　者：陈浩[1] 苏剑[2] 王尚锦[1] 朱明雷[2] 

机构地区：[1]西安交通大学能动学院,西安710049 [2]西安交通大学数学与统计学院,西安710049

出　　处：《工程数学学报》2013年第2期231-242,共12页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11001216;11171269;11272251);973资助项目子课题(2011CB706505)~~

摘　　要：工程实际中的许多间断问题,例如空气动力学中的激波问题,其数学模型大都是非线性双曲守恒律方程.本文在Runge-Kutta间断Galerkin(RKDG)框架下,结合h型自适应方法处理了一维非线性守恒律方程初值问题和初边值问题.此方法不仅能准确描述间断的出现和位置,而且还能在间断附近适当加密网格,提高计算效率.最后,数值算例验证了算法的有效性.Some discontinuous problems like the shock wave problem of aerodynamics can be described by a nonlinear hyperbolic conservation law. In this paper, we present a adap- tive discontinuous Galerkin method for the initial value and initial-boundary value problem of one-dimensional nonlinear hyperbolic conservation law. The method introduces a h-adaptive strategy in the framework of Runge-Kutta discontinuous Galerkin finite element （RKDG）. Then the appearance and position of discontinuity is captured by the method, and the mesh is prop- erly refined near the discontinuity to improve calculation efficiency. Finally, the correctness of the propose results is verified by numerical examples.

关 键 词：双曲守恒律方程 间断Galerkin有限元 h自适应方法 

分 类 号：O343[理学—固体力学]