Kinetic schemes for the ultra-relativistic Euler equations
Journal of Computational Physics
Second-order accurate kinetic schemes for the ultra-relativistic Euler equations
Journal of Computational Physics
Simulation of multicomponent flows using high order central schemes
Applied Numerical Mathematics
A matrix stability analysis of the carbuncle phenomenon
Journal of Computational Physics
Kinetic flux-vector splitting schemes for the hyperbolic heat conduction
Journal of Computational Physics
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In this paper we are going to study the gas evolution dynamics of the exact and approximate Riemann solvers, e.g., the Flux Vector Splitting (FVS) and the Flux Difference Splitting (FDS) schemes. Since the FVS scheme and the Kinetic Flux Vector Splitting (KFVS) scheme have the same physical mechanism and similar flux function, based on the analysis of the discretized KFVS scheme the weakness and advantage of the FVS scheme are closely observed. The subtle dissipative mechanism of the Godunov method in the 2D case is also analyzed, and the physical reason for shock instability, i.e., carbuncle phenomena and odd-even decoupling, is presented.