Entropy stability of bicompact schemes in gas dynamics problems

Fully discrete bicompact schemes of fourth order of approximation in space are examined for entropy stability in gas dynamics problems. Expressions for entropy production rates of these schemes are derived. Qualitative estimations for the behavior of these rates are obtained. Entropy production rates of bicompact schemes of first and third order in time are numerically analyzed in case of one-dimensional Riemann test problems. Based on the results of this analysis, it is concluded whether bicompact schemes need an entropy correction or not.