On the influence of the choice of the numerical flow on the solution of problems with shock waves by the discontinuous Galerkin method

The paper compares various numerical flows in the calculation of flows with the presence of shock waves by first-order schemes and second-order DG method on schemes from the Quirk’s list, namely: the Quirk problem and its modifications, shock wave diffraction at a 90 degree angle, the problem of double Mach reflection. It is shown that the use of HLLC and Godunov’s numerical flows in calculations can lead to instability, the Rusanov-Lax-Friedrichs flow leads to high dissipation of the calculation. The most versatile in carrying out production calculations are hybrid numerical flows, which allow suppressing the development of instabilities and maintaining the accuracy of the method.