An Examination of Homentropic Euler Equations with Averaged Characteristics

TL;DR

This paper introduces the characteristically averaged homentropic Euler (CAHE) equations, analyzing their mathematical properties, shock speeds, solutions to the Riemann problem, and comparing numerical behaviors with traditional homentropic Euler equations.

Contribution

It presents the formulation, existence, and uniqueness proofs for the CAHE equations, along with shock speed analysis and numerical comparisons.

Findings

CAHE equations have well-posed solutions.

Shock speeds are explicitly determined for CAHE.

Numerical simulations show differences in behavior between homentropic Euler and CAHE equations.

Abstract

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.