Artificial viscosity to cure the shock instability in high-order Godunov-type schemes
For computational fluid dynamics practitioners using high-order shock-capturing schemes, this work offers a practical fix for a known numerical instability, but the approach is incremental and requires tuning.
This study extends an artificial viscosity approach to cure shock instability (carbuncle phenomenon) in high-order Godunov-type schemes, adjusting the principal coefficient and providing suggestions to reduce post-shock oscillations, validated through numerous test problems.
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.