Simplified artificial viscosity approach for curing the shock instability

Abstract

The artificial viscosity approach for curing the carbuncle phenomenon and suppressing post-shock oscillations has recently been presented and successfully tested on both first-order and high-order Godunov-type schemes. This approach introduces some dissipation in the form of the right-hand side of Navier–Stokes equations into the basic method of solving Euler equations. The current study presents a simplified form of the artificial viscosity that is comparable to the original one in its efficiency. We also discuss the distinctive features of the artificial viscosity approach as compared to other ways of curing the carbuncle phenomenon. In addition, the accuracy of several approximate Riemann solvers has been examined in combination with the artificial viscosity approach.