%0 Journal Article
%T 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<br>Dissipative Measure-Valued Solutions of High Order Numerical Schemes for Compressible Euler Equations with Maximum Density Constraints
%A 皇晓燕
%A 华嘉乐
%J Pure Mathematics
%P 241-254
%@ 2160-7605
%D 2025
%I Hans Publishing
%R 10.12677/PM.2025.155173
%X 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p<sup>δ</sup>,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。<br>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 p<sup>δ</sup>(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.
%K 可压欧拉方程，耗散测度值解，高阶精度，最大密度限制<br>Compressible Euler System
%K Dissipative Measure-Valued Solution
%K High Order Accuracy
%K Maximum Density Constraint
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=115862