无波动、无自由参数的耗散差分格式

本文通过对“模型问题”的研究发现,在激波附近差分解的虚假波动与差分方程的修正方程式的三阶色散项相关。如果适当地调节色散项的系数使之过激波时该系数按要求变号,则可完全抑制激波附近虚假的波动。 在以上发现的基础上,提出了一个有效的无自由参数、无波动的差分格式。文中证明,这个格式就是“TVD格式”,亦可视为格式的推广。 文中对许多二维、三维流动作了计算,结果表明,本文的格式应用方便且可得到满意的结果,对激波有较高的分辨能力。

NON-OSCILLATORY AND NON-FREE-PARAMETER DISSIPATION DIFFERENCE SCHEME

Through a model study,the spurious oscillations occuring near shock waves with finite difference equations were found to be related to the dispersion terms in the corresponding modified differential equation.If the signs of the dispersion coefficients are properly adjusted so that the signs change across waves,the undisirable oscillations can be totally suppressed and this fact is also in conformity with the requirement of the second law in thermodynamics,i.e.with this artifice the entropy of heat isolated system increases.Based on the above findings,an efficient finite difference scheme is developed and in fact it is a "TVD" scheme though much simpler.Our scheme is related to the Godunov's,and may be considered as its extension.Finally,numerical results of two-and three-dimensional flows are given with the present numerical schemes.It is shown that the algorithm is efficient and robust.