Combined Monotone Bicompact Scheme of Higher Order Accuracy in Domains of Influence of Nonstationary Shock Waves

Abstract

A new method is proposed for constructing a 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 the fourth order of approximation in space obtained for different time steps in the entire computational domain. This construction method is much simpler than a previously proposed method. Test calculations are presented that demonstrate the advantages of the new scheme compared to the WENO5 scheme of the fifth order of approximation in space and the third order of approximation in time.