Abstract

We consider a multidimensional hyperbolic quasi-gasdynamic system of differential equations of the second order in time and space linearized on a constant solution (with an arbitrary velocity). For the linearized system with constant coefficients, we study the implicit three-level weighted and two-level vector difference schemes. The important domination property of the operator of viscous terms (with no allowance for the relaxation parameter) over the operator of convective terms is derived. We apply this property to prove by the energy method that, regardless of the Mach number, our implicit schemes on a nonuniform rectangular mesh (without any conditions on the mesh steps) are stable with respect to the initial data and the right-hand side uniformly in time and the relaxation parameter.

中文翻译：

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线性双曲拟气动力学方程组隐式差分格式的稳定性

摘要

我们考虑在恒定解（具有任意速度）下线性化的时空二阶微分方程的多维双曲拟气体动力学系统。对于具有恒定系数的线性化系统，我们研究隐式三级加权和两级矢量差分方案。得出粘性项算子（不考虑松弛参数）对流项算子的重要支配性质。我们应用此属性通过能量方法证明，无论马赫数如何，我们在非均匀矩形网格上的隐式方案（网格步长没有任何条件）相对于初始数据和右侧都是稳定的时间和松弛参数。