An optimized contact upwind flux splitting scheme based on characteristics

The Flux Vector Splitting (FVS) scheme tends to produce numerical transition zones and nonphysical oscillations when initialized with mathematical discontinuities. Although the Upwind Flux Scheme based on Characteristics (UFSC) can alleviate such errors, it still exhibits limitations in handling stationary contact discontinuities and high-Mach number shock waves. To overcome these issues, this paper proposes the Optimized-Contact UFSC (OC-UFSC), which achieves strict preservation of stationary contact discontinuities through an improved decoupling strategy. Furthermore, by incorporating a shock detector with the Van Leer scheme, a hybrid scheme OC-UFSC+V, is constructed to enhance stability under high-Mach number shocks. Comparative analyses against the FVS and Flux Difference Splitting (FDS) schemes in both one- and two-dimensional benchmark tests demonstrate that OC-UFSC+V resolves contact discontinuities sharply, expansion waves, and shock waves. Compared with the FVS scheme, it preserves the accuracy of linear and quadratic flows, matches the resolution of FDS schemes, and effectively avoids the common Carbuncle phenomenon in FDS. Overall, OC-UFSC+V exhibits superior resolution and stability.