Entropy Stability of Bicompact Schemes in Gas Dynamics Problems

Fully discrete bicompact schemes of the fourth order of approximation in space are investigated for entropy stability in problems of gas dynamics. Expressions for the rate of entropy production in these schemes are derived. Qualitative estimates are obtained for the behavior of this quantity. On the example of one-dimensional Riemann test problems, a numerical analysis of the entropy production rate for bicompact schemes of the first and third orders of approximation in time is carried out. From the results of this analysis, it is concluded whether any entropy correction is necessary for bicompact schemes.