Numerical modeling of compressible mixing layers with a bicompact scheme

A bicompact scheme for the Navier-Stokes equations is considered in the case of a compressible heat-conducting fluid. The scheme is constructed using the splitting by physical processes, has the approximation of fourth order in space and second in time. New, conservative formulas are derived for transitions between two different representations of numerical solution in bicompact schemes for hyperbolic and parabolic equations. The parallel implementation of the bicompact scheme is tested for strong scalability. The bicompact scheme is applied to the three-dimensional direct numerical simulation of the mixing layer with convective Mach numbers of 0.4 and 0.8. In the calculated flows, the zone of turbulent mixing is resolved in detail, and the phenomena observed in experiments are adequately reproduced. Good quantitative agreement is demonstrated with the simulations carried out by other authors.