Initial discontinuity-induced nonphysical oscillations in finite volume method and its suppression algorithm

The finite volume method is widely applied in computational fluid dynamics engineering practices. Particularly in the computation of compressible flow fields, discontinuous structures often evolve into numerical transition zones spanning multiple grid points. During this process, nonphysical oscillations parallel to the discontinuity are generated and are regularly distributed. Discontinuities such as shock waves are defined by characteristic Euler equations, and the UFSC (Upwind Flux Scheme based on Characteristics) scheme is a flux computation method constructed based on the characteristic upwind properties derived from the equations. This paper presents numerical examples comparing the performance of the UFSC scheme with other conventional flux-splitting schemes (such as Steger–Warming, van Leer) under the finite volume method. The results show that the UFSC scheme effectively eliminates the nonphysical oscillations induced by the initial contact discontinuities in the flux vector splitting scheme. Additionally, it significantly reduces the amplitude of the disturbances caused by the initial shock wave. Moreover, for hypersonic flow problems, the UFSC scheme, compared to Roe and other FDS (flux difference splitting) schemes, does not exhibit shock instability, demonstrating excellent numerical stability. The UFSC scheme shows strong stability in both strongly discontinuous and continuous flow fields, demonstrating its practical value in engineering computations.