Combined multidimensional bicompact scheme with higher order accuracy in domains of influence of nonstationary shock waves

For the first time, a method is proposed for constructing a multidimensional combined shock-capturing scheme that monotonically localizes shock wave fronts and, at the same time, has increased accuracy in smoothness regions of calculated generalized solutions. In this method, the solution of the combined scheme is constructed using monotonic solutions of a bicompact scheme of the first order of approximation in time and fourth order of approximation in space. The solutions are obtained for different time steps in the entire computational domain. This construction method is much simpler than other techniques for constructing combined schemes with similar properties. The results of test calculations are presented, which demonstrate the high accuracy of the proposed combined scheme as applied to a multidimensional flow with shock waves.