最大密度限制下可压欧拉方程高阶精度数值格式的耗散测度值解
Dissipative Measure-Valued Solutions of High Order Numerical Schemes for Compressible Euler Equations with Maximum Density Constraints
摘要: 本文主要考虑带有最大密度限制的可压欧拉方程组的初边值问题，这种密度限制依据一个奇性压强给出。文章通过引入带有截断参数δ>0的近似压强pδ,并建立合适的先验估计，得到了欧拉方程数值格式与其原方程的一致性公式。同时，研究了δ→0时的极限，证明数值解可以收敛到耗散测度值解。
Abstract: This paper primarily focuses on the initial-boundary value problem of the compressible Euler equations with a maximum density constraint, where the density constraint is given by a singular pressure. By introducing an approximate pressure pδ(p） with a truncation parameterδ>0. and establishing appropriate the priori estimates, the paper derives the consistency formulas between the numerical schemes of the Euler equations and the original equations. Moreover, the limit as δ→0 is investigated, and it is proven that the numerical solutions can converge to dissipative measure-valued solutions.
文章引用：皇晓燕, 华嘉乐. 最大密度限制下可压欧拉方程高阶精度数值格式的耗散测度值解[J]. 理论数学, 2025, 15(5): 241-254. https://doi.org/10.12677/PM.2025.155173

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