A linear preserving flux splitting scheme based on eigenvalue upwind characteristics

Flux vector splitting (FVS) schemes tend to induce nonphysical oscillations in the numerical transition region when handling initial conditions with mathematical discontinuities. In high-Mach-number flows, such small oscillations may significantly disturb the flow-field variables. The existing OC-UFSC scheme can effectively suppress nonphysical oscillations induced by shock discontinuities and achieve strict preservation of density discontinuities; however, it still exhibits certain limitations in preserving linear velocity fields. To address this issue, this study proposed a novel LP-OC-UFSC scheme capable of preserving both linear velocity and density fields. By employing a spatial decoupling strategy, the scheme achieved strict preservation of linear distributions of both velocity and density. Numerical results demonstrate that the LP-OC-UFSC scheme fully retains the capability of the original OC-UFSC scheme to suppress nonphysical oscillations induced by shock discontinuities, as well as its ability to strictly preserve density contact discontinuities. In supersonic flow simulations, the proposed scheme exhibits excellent robustness and avoids the carbuncle phenomenon commonly encountered in FDS schemes. In viscous flow simulations of the flat-plate boundary layer, its accuracy is significantly higher than that of FVS schemes and the original OC-UFSC scheme, comparable to that of FDS-type schemes, and superior to the entropy-corrected Roe scheme. The three-dimensional double-ellipsoid test case further verifies the method's capability to simulate complex shock wave flows and its engineering applicability on both structured and unstructured grids. The proposed LP-OC-UFSC scheme provides an effective approach to resolving the trade-off between stability and accuracy in high-Mach-number flow simulations, offering reference value for high-fidelity numerical simulations of complex engineering flows.