  In this paper, continuous research is undertaken to explore the underlying
mechanism of numerical shock instabilities of Godunov-type schemes for strong
shocks. By conducting dissipation analysis of Godunov-type schemes and a
sequence of numerical experiments, we are able to clarify that the instability
may be attributed to insufficient entropy production inside the numerical shock
structure. As a result, a general entropy-control technique for improving the
robustness of various Godunov-type schemes at strong shocks is developed. It
plays a part in guaranteeing that enough entropy is produced inside the
numerical shock structure. Furthermore, such a modified approach does not
introduce any additional numerical dissipation on linear degenerate waves to
suppress the shock instability. Numerical results that are obtained for various
test cases indicate that the proposed methods have a good performance in terms
of accuracy and robustness.
