Preconditioned methods for solving the incompressible low speed compressible equations
Journal of Computational Physics
On Godunov-type methods for gas dynamics
SIAM Journal on Numerical Analysis
The behavior of flux difference splitting schemes near slowly moving shock waves
Journal of Computational Physics
The application of preconditioning in viscous flows
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
An Accurate and Robust Flux Splitting Scheme for Shock and Contact Discontinuities
SIAM Journal on Scientific Computing
Mass flux schemes and connection to shock instability
Journal of Computational Physics
Methods for the accurate computations of hypersonic flows: I. AUSMPW + scheme
Journal of Computational Physics
Journal of Computational Physics
Very simple, carbuncle-free, boundary-layer-resolving, rotated-hybrid Riemann solvers
Journal of Computational Physics
A front-tracking/ghost-fluid method for fluid interfaces in compressible flows
Journal of Computational Physics
An investigation of interface-sharpening schemes for multi-phase mixture flows
Journal of Computational Physics
On physics-based preconditioning of the Navier-Stokes equations
Journal of Computational Physics
Analysis of Godunov type schemes applied to the compressible Euler system at low Mach number
Journal of Computational Physics
The influence of cell geometry on the Godunov scheme applied to the linear wave equation
Journal of Computational Physics
High-order finite-volume methods for the shallow-water equations on the sphere
Journal of Computational Physics
A Runge-Kutta discontinuous Galerkin approach to solve reactive flows: The hyperbolic operator
Journal of Computational Physics
A Runge-Kutta discontinuous Galerkin approach to solve reactive flows: The hyperbolic operator
Journal of Computational Physics
Journal of Computational Physics
Multi-dimensional limiting for high-order schemes including turbulence and combustion
Journal of Computational Physics
MCore: A non-hydrostatic atmospheric dynamical core utilizing high-order finite-volume methods
Journal of Computational Physics
Pressure-velocity coupling allowing acoustic calculation in low Mach number flow
Journal of Computational Physics
Journal of Computational and Applied Mathematics
An Eulerian-Lagrangian moving immersed interface method for simulating burning solids
Journal of Computational Physics
Journal of Computational Physics
An accurate low-Mach scheme for a compressible two-fluid model applied to free-surface flows
Journal of Computational Physics
Hi-index | 31.54 |
In this paper, we present ideas and procedure to extend the AUSM-family schemes to solve flows at all speed regimes. To achieve this, we first focus on the theoretical development for the low Mach number limit. Specifically, we employ asymptotic analysis to formally derive proper scalings for the numerical fluxes in the limit of small Mach number. The resulting new scheme is shown to be simple and remarkably improved from previous schemes in robustness and accuracy. The convergence rate is shown to be independent of Mach number in the low Mach number regime up to M"~=0.5, and it is also essentially constant in the transonic and supersonic regimes. Contrary to previous findings, the solution remains stable, even if no local preconditioning matrix is included in the time derivative term, albeit a different convergence history may occur. Moreover, the new scheme is demonstrated to be accurate against analytical and experimental results. In summary, the new scheme, named AUSM^+-up, improves over previous versions and eradicates fails found therein.