Initial discontinuity induced non-physical fluctuation and its elimination algorithm

When the shock capturing method is used to solve inviscid compressible flow with a mathematical discontinuity as the initial condition, the discontinuity will gradually evolve into a numerical transition region across several grid points, and non-physical fluctuations in two directions parallel to the discontinuity can be induced in this process. The initial shock, which is calculated as the initial condition, satisfies the Euler equation, while the flow field parameters should satisfy the modified equations, such conflict might be the reason for the initial shock-induced non-physical fluctuations. As the discontinuities such as shock waves are defined by the characteristic lines of the Euler equation, an upwind flux scheme based on characteristics (UFSC) is proposed in the present study. Using several conventional conservation flux schemes as a reference, the UFSC can eliminate the non-physical fluctuations induced by the Steger-Warming and Van Leer schemes at the initial contact discontinuities, and can reduce the amplitude of the initial shock-induced disturbances. For the flow field in smooth regions, the computational results from the UFSC and conserved flux scheme are similar, but larger pressure peaks appear near the strong shock. To overcome this defect, a hybrid scheme UFSC+S is constructed, which uses the Steger-Warming for calculation in the shock region and the UFSC in other regions.