Abstract

We study an explicit two-level symmetric (in space) finite-difference scheme for the multidimensional barotropic gas dynamics system of equations with quasi-gasdynamic regularization linearized at a constant solution (with an arbitrary velocity). A criterion and both necessary and sufficient conditions for the L²-dissipativity of the solutions to the Cauchy problem for the scheme are derived by the spectral method. In them, the Courant number is uniformly bounded with respect to the Mach number.

中文翻译：

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正压气体动力学方程组的线性拟线性正则化有限差分格式的L 2耗散性

摘要

我们为多维正压气体动力学方程组研究了一个显式的两级对称（空间）有限差分方案，该方程组具有以恒定解（具有任意速度）线性化的准气体动力学正则化方程。通过谱方法推导了该方案的柯西问题的解的L ²耗散性的判据和充要条件。在其中，库兰特数相对于马赫数统一界定。