Nonlinear acoustic propagation in homentropic perfect gases: A numerical study

A study of nonlinear acoustic waves in a homentropic perfect gas is presented. Conservation laws for the Euler and Lighthill–Westervelt equations are constructed and solved numerically using a Godunov-type finite-difference scheme. Simulations are carried out in the context of two initial-boundary-value problems (IBVP)s—one resulting in finite-time, and the other in infinite-time, blow-up at the wavefront. Additionally, analytical results are presented to support the numerical findings.