Abstract: As a continuous effort to understand the Godunov-type schemes, following the paper "Projection Dynamics in Godunov-type Schemes" (Jcp Vol.142, 412-427, 1998), in this paper we are going to study the gas evolution dynamics of the exact and approximate Riemann solvers. More specifically, the underlying dynamics of the Flux Vector Splitting (FVS) and Flux Difference Splitting (FDS) schemes will be analyzed. Since the FVS scheme and the Kinetic Flux Vector Splitting (KFVS) scheme have the same physical mechanism and numerical formulations, based on the governing equation of the discretized KFVS scheme, the weakness and advantages of the FVS scheme are clearly observed. Also, in this paper, the implicit equilibrium assumption in the Godunov flux will be analyzed. Due to the numerical shock thickness related to the cell size, the numerical scheme should be able to capture both equilibrium and non-equilibrium flow behavior in smooth and discontinuous regions, The Godunov flux basically lacks the mechanism to capture nonequilibrium effects in the artificially enlarged numerical shock region and to stabilize the numerical shock structure. Consequently, the Godunov method is exposed to the possible spurious solutions, such as the carbuncle phenomena and odd-even decoupling, once the dissipation provided in the projection stage is not enough.
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