CAJ | 학술논문

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-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.
고필료관우이유수항률적대시간보장Godunov방법.해방법시관우일유문제적자연추엄.증명료문중급출적수치류함수하,해방법시수항적.진-보환급출료근사Riemann해응만족적조건,병차증명료이용만족저사조건적근사Riemann해적대시간보장Godunov방법수항.최후,보충증명료만족저사조건적근사Riemann해시만족적조건적.
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.