  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.
