Preconditioned methods for solving the incompressible low speed compressible equations
Journal of Computational Physics
Boltzmann type schemes for gas dynamics and the entropy property
SIAM Journal on Numerical Analysis
Journal of Computational Physics
A projection method for locally refined grids
Journal of Computational Physics
Journal of Computational Physics
Numerical simulation of the homogeneous equilibrium model for two-phase flows
Journal of Computational Physics
A sequel to AUSM, Part II: AUSM+-up for all speeds
Journal of Computational Physics
Journal of Computational Physics
An All-Speed Roe-type scheme and its asymptotic analysis of low Mach number behaviour
Journal of Computational Physics
The influence of cell geometry on the accuracy of upwind schemes in the low mach number regime
Journal of Computational Physics
The influence of cell geometry on the Godunov scheme applied to the linear wave equation
Journal of Computational Physics
The momentum interpolation method based on the time-marching algorithm for All-Speed flows
Journal of Computational Physics
A low-Mach number fix for Roe's approximate Riemann solver
Journal of Computational Physics
Pressure-velocity coupling allowing acoustic calculation in low Mach number flow
Journal of Computational Physics
An Asymptotic-Preserving all-speed scheme for the Euler and Navier-Stokes equations
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 | 31.48 |
We propose a theoretical framework to clearly explain the inaccuracy of Godunov type schemes applied to the compressible Euler system at low Mach number on a Cartesian mesh. In particular, we clearly explain why this inaccuracy problem concerns the 2D or 3D geometry and does not concern the 1D geometry. The theoretical arguments are based on the Hodge decomposition, on the fact that an appropriate well-prepared subspace is invariant for the linear wave equation and on the notion of first-order modified equation. This theoretical approach allows to propose a simple modification that can be applied to any colocated scheme of Godunov type or not in order to define a large class of colocated schemes accurate at low Mach number on any mesh. It also allows to justify colocated schemes that are accurate at low Mach number as, for example, the Roe-Turkel and the AUSM^+-up schemes, and to find a link with a colocated incompressible scheme stabilized with a Brezzi-Pitkaranta type stabilization. Numerical results justify the theoretical arguments proposed in this paper.