可压欧拉方程高精度数值格式耗散测度值解的收敛性
Convergence of Dissipative Measure-Valued Solutions for High Order Numerical Schemes of the Compressible Euler Equations
摘要: 本文主要考虑可压欧拉方程组的初边值问题。研究了两类具有高阶精度的熵稳定有限体积格式的收敛性，通过对数值解建立合适的一致性估计，证明随着步长 h → 0，若数值解的密度是远离真空且有界的，则由这两类熵稳定数值格式构造的解可以生成耗散测度值解。
Abstract: In this paper, we primarily consider the initial boundary value problem for compressible Euler equations. We study the convergence of two classes of high-order accurate entropy stable finite volume schemes. By establishing appropriate the priori estimates for the numerical solutions, we prove that as the step size h → 0, the solutions constructed by these two types of entropy stable numerical schemes can generate dissipative measure-valued solutions, provided that the density of the approximate solutions is bounded away from vacuum and bounded above.
文章引用：皇晓燕, 华嘉乐. 可压欧拉方程高精度数值格式耗散测度值解的收敛性[J]. 理论数学, 2025, 15(4): 458-471. https://doi.org/10.12677/pm.2025.154146

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