二维双曲守恒律的大时间步长Godunov方法(英文)  

Large Time Step Godunov Method for 2-D Conservation Laws

作　　者：温海瑞[1] 王靖华[2] 

机构地区：[1]北京理工大学数学系,北京100081 [2]中国科学院数学与系统科学研究院,北京100190

出　　处：《应用泛函分析学报》2010年第2期97-109,共13页Acta Analysis Functionalis Applicata

基　　金：Supported by National Natural Foundation of China(10671116,10871133)

摘　　要：考虑了关于二维守恒律的大时间步长Godunov方法.该方法是关于一维问题的自然推广.证明了文中给出的数值流函数下,该方法是守恒的.进一步还给出了近似Riemann解应满足的条件,并且证明了利用满足这些条件的近似Riemann解的大时间步长Godunov方法守恒.最后,补充证明了满足这些条件的近似Riemann解是满足熵条件的.The large time step（LTS） Godunov scheme for 2-D conservation laws is studied, which is a generalization of this kind of schemes for 1-D problems devised by LeVeque. We show that the 2-D large time step Godunov scheme can be written in conservation form, thus the limit of the solution is a weak solution due to Lax-Wendroff theorem. Then give some conditions for approximate solutions, and show that the large time step Godunov scheme can be written in conservation form replacing the true Riemann solutions by approximate Riemann solutions. And at the end of this paper, detail the proof of the approximate solver satisfying the entropy inequality motivated by Wendroff.

关 键 词：双曲守恒律 守恒形式 Godunov方法 RIEMANN问题 

分 类 号：O175.29[理学—数学] O241.82[理学—基础数学]