具有平均特征的各向同性Euler方程的研究
An Examination of Homentropic Euler Equations with Averaged Characteristics
摘要：
本文研究了等熵欧拉方程在特征空间平均化后的性质。新方程被称为特征平均等熵欧拉（CAHE）方程。给出了修正方程的存在唯一性证明。确定了CAHE方程的激波速度。黎曼问题的审查和一般形式的解决方案。最后，对等熵Euler方程和CAHE方程进行了数值模拟，并对两组方程的行为进行了比较。
英文摘要：
This paper examines the properties of the homentropic Euler equations when the characteristics of the equations have been spatially averaged. The new equations are referred to as the characteristically averaged homentropic Euler (CAHE) equations. An existence and uniqueness proof for the modified equations is given. The speed of shocks for the CAHE equations are determined. The Riemann problem is examined and a general form of the solutions is presented. Finally, numerically simulations on the homentropic Euler and CAHE equations are conducted and the behaviors of the two sets of equations are compared.
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