Computer Methods in Applied Mechanics and Engineering
SIAM Journal on Scientific and Statistical Computing
Numerical Instablilities in Upwind Methods: Analysis and Cures for the “Carbuncle” Phenomenon
Journal of Computational Physics
A matrix stability analysis of the carbuncle phenomenon
Journal of Computational Physics
Very simple, carbuncle-free, boundary-layer-resolving, rotated-hybrid Riemann solvers
Journal of Computational Physics
SIAM Journal on Numerical Analysis
High-order entropy stable finite difference schemes for nonlinear conservation laws: Finite domains
Journal of Computational Physics
Entropy-Stable Schemes for the Euler Equations with Far-Field and Wall Boundary Conditions
Journal of Scientific Computing
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In this paper, an entropy-consistent flux is developed, continuing from the work of the previous paper. To achieve entropy consistency, a second and third-order differential terms are added to the entropy-conservative flux. This new flux function is tested on several one dimensional problems and compared with the original Roe flux. The new flux function exactly preserves the stationary contact discontinuity and does not capture the unphysical rarefaction shock. For steady shock problems, the new flux predicts a slightly more diffused profile whereas for unsteady cases, the captured shock is very similar to those produced by the Roe- flux. The shock stability is also studied in one dimension. Unlike the original Roe flux, the new flux is completely stable which will provide as a candidate to combat multidimensional shock instability, particularly the carbuncle phenomenon.