一维Euler方程和均质Euler方程的一种新正则化
A New Regularization of the One-Dimensional Euler and Homentropic Euler Equations
摘要：
本文研究了一种平均技术，其中的非线性通量项展开和对流速度通过低通滤波器。这是意图，这种修改的非线性通量项将导致无粘正则化的均熵欧拉方程和欧拉方程。给出了这种方法的物理动机，并导出了一种通用的方法，然后将其应用于等熵欧拉方程和欧拉方程。对这些修正方程进行了检验，发现它们与原方程具有相同的守恒性和行波解。当平均值减小时，证明了解收敛于原方程的弱解。最后，进行数值模拟发现，正则化方程出现光滑和捕捉相关的行为在激波管模拟。
英文摘要：
This paper examines an averaging technique in which the nonlinear flux term is expanded and the convective velocities are passed through a low-pass filter. It is the intent that this modification to the nonlinear flux terms will result in an inviscid regularization of the homentropic Euler equations and Euler equations. The physical motivation for this technique is presented and a general method is derived, which is then applied to the homentropic Euler equations and Euler equations. These modified equations are then examined, discovering that they share the conservative properties and traveling wave solutions with the original equations. As the averaging is diminished it is proven that the solutions converge to weak solutions of the original equations. Finally, numerical simulations are conducted finding that the regularized equations appear smooth and capture the relevant behavior in shock tube simulations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
