Solution Verification of Anomalous Waves in Nonideal Gases

Abstract

Abstract Solution verification methods for anomalous waves in inviscid and viscous van der Waals gases are presented. Anomalous waves are admissible in a single gas phase material when isentropes are concave, rendering the sound speed to have the unusual feature of decreasing with increasing density. The anomalous waves considered include rarefaction shocks and continuous compression fans. A previously known exact solution of inviscid continuous fans with a van der Waals equation of state is applied to anomalous waves. An exact solution for viscous shocks in an ideal gas is described and utilized for verification of the viscous numerical solutions. Solutions and simulations of viscous and inviscid van der Waals gases in shock tubes are presented with both conventional and anomalous waves. Shock tube solutions are used for verification of numerical simulations. Highly resolved viscous solutions are obtained with a simple explicit Euler time advancement scheme coupled with a second-order central spatial discretization. Inviscid simulations are performed with a third-order Runge–Kutta method in time and a fifth-order mapped weighted essentially nonoscillatory (WENO5M) discretization. The WENO5M method is novelly supplemented with a global Lax–Friedrichs flux-splitting in space, as local flux-splitting methods fail when changes in the sound speed are nonmonotonic.