Shock stability of a novel flux splitting scheme

This article introduced the HLL-CPS-T flux splitting scheme, which is characterized by low dissipation and robustness. A detailed theoretical analysis of the dissipation and shock stability of this scheme was provided. In comparison to Toro's TV flux splitting scheme, the HLL-CPS-T scheme not only exhibits accurate capture of contact discontinuity, but also demonstrates superior shock stability, as evidenced by its absence of 'carbuncle' phenomenon. Through an examination of the disturbance attenuation properties of physical quantities in the TV and HLL-CPS-T schemes, an inference was derived: The shock stability condition for an upwind method in the velocity perturbation was damped. Theoretical analysis was given to verify the reasonableness of this inference. Numerical experiments were carefully selected to test the robustness of the new splitting scheme.