Hybrid flux-splitting schemes for a two-phase flow model
Journal of Computational Physics
Cures for the shock instability: development of a shock-stable Roe scheme
Journal of Computational Physics
Concepts and Application of Time-Limiters to High Resolution Schemes
Journal of Scientific Computing
Hybrid flux-splitting schemes for a common two-fluid model
Journal of Computational Physics
Management of discontinuous reconstruction in kinetic schemes
Journal of Computational Physics
A matrix stability analysis of the carbuncle phenomenon
Journal of Computational Physics
A sequel to AUSM, Part II: AUSM+-up for all speeds
Journal of Computational Physics
Diffusion regulation for Euler solvers
Journal of Computational Physics
DIMEX Runge-Kutta finite volume methods for multidimensional hyperbolic systems
Mathematics and Computers in Simulation
Improving shock irregularities based on the characteristics of the MHD equations
Journal of Computational Physics
Modelling blast loads on buildings in complex city geometries
Computers and Structures
Relaxation schemes for the calculation of two-phase flow in pipes
Mathematical and Computer Modelling: An International Journal
Block-spectral mapping for multi-scale solution
Journal of Computational Physics
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A flux splitting scheme (AUSMDV) has been constructed with an aim at removing numerical dissipation of the Van Leer-type flux vector splittings on a contact discontinuity. The obtained scheme is also recognized as an improved advection upstream splitting method (AUSM) by Liou and Steffen. The proposed scheme has the following favorable properties: accurate and robust resolution for shock and contact (steady and moving) discontinuities; conservation of enthalpy for steady flows; algorithmic simplicity; and easy extension to general conservation laws such as that for chemically reacting flows. A simple shock fix is presented to cure the numerical shock instability associated with the ``carbuncle phenomenon'' and an entropy fix to remove an expansion shock or glitch at the sonic point. Extensive numerical experiments were conducted to validate the proposed scheme for a wide range of problems, and the results are compiled for comparison with several recent upwind methods.