Artificial viscosity to cure the shock instability in high-order Godunov-type schemes

Abstract

The artificial viscosity approach for curing the carbuncle phenomenon (a numerical problem, also known as the shock instability) in shock-capturing methods has been recently presented and successfully tested on the first-order schemes in two- and three-dimensional simulations. The present study extends the proposed approach to the case of using high-order Godunov-type schemes. Several implementations of well-known schemes were selected for the study. They involve the MUSCL and WENO data reconstructions in space along with the Runge–Kutta and Hancock-type time stepping techniques. Numerous computations of the Quirk-type test problems and other popular tests were performed to examine and tune the artificial viscosity approach as applied to the selected schemes. As a result of this study (1) the principal coefficient in the artificial viscosity model was adjusted and (2) some methodological suggestions for substantial weakening of the post-shock oscillations were stated.