Generalized Noh self-similar solutions of the compressible Euler equations for hydrocode verification

Abstract

A family of exact self-similar solutions of the compressible Euler equations developed for hydrocode verification is described. This family generalizes the classic Noh problem, which has served as a standard verification test of numerical methods for modeling inviscid compressible flows for three decades. This generalization allows finite pressure initial conditions, nearly arbitrary equations of state, and describes shocked compression as well as isentropic expansion and compression of the gas. In particular, the solutions describe a) the propagation of a finite-strength spherical isentropic expansion wave into a moving uniform gas, leaving behind either a core of uniform gas at rest or a vacuum/cavitation; b) the convergence of a finite-strength isentropic compression wave into a uniform gas or a collapse of a cavity in a finite-pressure gas (a compressible analog of the Rayleigh problem); and c) the expansion of a finite-strength accretion shock wave into a converging isentropic flow of stagnating gas. Our proposed verification test seeks to numerically reproduce all three of these stages of gas motion in a single simulation run. The successful verification of a high-order Godunov Eulerian hydrodynamics code is presented as an example of the expected use of this family of exact solutions.