On Godunov-type methods for gas dynamics
SIAM Journal on Numerical Analysis
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
On Godunov-type methods near low densities
Journal of Computational Physics
Use of a rotated Riemann solver for the two-dimensional Euler equations
Journal of Computational Physics
Journal of Computational Physics
Approximate Riemann solvers, parameter vectors, and difference schemes
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
High resolution schemes for hyperbolic conservation laws
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
Multidimensional dissipation for upwind schemes: stability and applications to gas dynamics
Journal of Computational Physics
Mass flux schemes and connection to shock instability
Journal of Computational Physics
A positive conservative method for magnetohydrodynamics based on HLL and Roe methods
Journal of Computational Physics
Numerical Instablilities in Upwind Methods: Analysis and Cures for the “Carbuncle” Phenomenon
Journal of Computational Physics
Methods for the accurate computations of hypersonic flows: I. AUSMPW + scheme
Journal of Computational Physics
Cures for the shock instability: development of a shock-stable Roe scheme
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
Affordable, entropy-consistent Euler flux functions II: Entropy production at shocks
Journal of Computational Physics
Hi-index | 31.45 |
In this paper, we propose new Euler flux functions for use in a finite-volume Euler/Navier-Stokes code, which are very simple, carbuncle-free, yet have an excellent boundary-layer-resolving capability, by combining two different Riemann solvers into one based on a rotated Riemann solver approach. We show that very economical Euler flux functions can be devised by combining the Roe solver (a full-wave solver) and the Rusanov/HLL solver (a fewer-wave solver), based on a rotated Riemann solver approach: a fewer-wave solver automatically applied in the direction normal to shocks to suppress carbuncles and a full-wave solver applied, again automatically, across shear layers to avoid an excessive amount of dissipation. The resulting flux functions can be implemented in a very simple and economical manner, in the form of the Roe solver with modified wave speeds, so that converting an existing Roe flux code into the new fluxes is an extremely simple task. They require only 7-14% extra CPU time and no problem-dependent tuning parameters. These new rotated fluxes are not only robust for shock-capturing, but also accurate for resolving shear layers. This is demonstrated by an extensive series of numerical experiments with standard finite-volume Euler and Navier-Stokes codes, including various shock instability problems and also an unstructured grid case.