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解守恒律方程组的一类新差分格式

于欣   

  1. 北京大学数学系
  • 出版日期:1987-03-14 发布日期:1987-03-14

于欣. 解守恒律方程组的一类新差分格式[J]. 计算数学, 1987, 9(3): 251-261.

A CLASS OF NEW SCHEMES FOR CONSERVATION LAWS

  1. Yu Xin Department of Mathematics. Beijing University
  • Online:1987-03-14 Published:1987-03-14
初值问题(1.1)的一个主要特点是:即使初值函数w_0(x)是充分光滑的,大范围的古典解也不一定存在.用激波捕捉法(即“穿行”法)数值求解(1.1)通常精度较低.六十年代出现了一些二阶精度的差分格式.例如Lax-Wendroff格式.但这些格式的差分解通常在激波等间断附近产生较大的过头和低亏现象.本文用一个二阶精度的差分格式修正
In this paper, we present a class of new explicit nonlinear finite difference schemes of se-cond order accuracy for conservation laws (1.1) by modifying a nonoscillatory first order ac-curate scheme by a second order accurate scheme such as Lax-Wendroff scheme. The numericalsolutions obtained in the calculation of a Riemann problem achieve high precision while havingno oscillations near the shocks.
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[3] C. W. Hirt, Heuristic stability theory for finitedifference equations, J. Comput. Phys., 2: 4(1968) ,339--355.
[4] J. von Neumann, R. D. Richtmyer, A method for the numerical calculation of hydrodynamic shocks,J. Appl. Phys., 21: 3(1950) , 232--237.
[5] 于欣,双曲型守恒律方程组的高分辨率全变差不增格式,高等学校计算数学学报,待发表.
[6] 于欣,双曲型守恒律方程组的高分辨率全变差不增格式,北京大学硕士论文,1985.
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