Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
SIAM Journal on Scientific and Statistical Computing
A front-tracking method for viscous, incompressible, multi-fluid flows
Journal of Computational Physics
A continuum method for modeling surface tension
Journal of Computational Physics
Modelling merging and fragmentation in multiphase flows with SURFER
Journal of Computational Physics
A level set approach for computing solutions to incompressible two-phase flow
Journal of Computational Physics
A multiphase Godunov method for compressbile multifluid and multiphase flows
Journal of Computational Physics
Volume-of-fluid interface tracking with smoothed surface stress methods for three-dimensional flows
Journal of Computational Physics
A five-equation model for the simulation of interfaces between compressible fluids
Journal of Computational Physics
Discrete equations for physical and numerical compressible multiphase mixtures
Journal of Computational Physics
A sequel to AUSM, Part II: AUSM+-up for all speeds
Journal of Computational Physics
An All-Speed Roe-type scheme and its asymptotic analysis of low Mach number behaviour
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
An Asymptotic-Preserving all-speed scheme for the Euler and Navier-Stokes equations
Journal of Computational Physics
Hi-index | 31.45 |
Classical approximate Riemann solvers are known to be too much dissipative in the low-Mach number regime. For this reason, since the Mach number in liquids is generally very small, usual upwind schemes may provide inaccurate solutions when applied to the simulation of two-phase flows. In this paper, to circumvent this difficulty while keeping a compressible model for the description of both gas and liquid, an original accurate low-Mach scheme is introduced and theoretically studied. Extending some ideas already used for the gas dynamics system, the proposed scheme is based on a centred formulation for the pressure gradient term in the momentum equation and on the introduction of a stabilising term proportional to the pressure difference between two neighbouring cells. The scheme stability is ensured, and theoretically proved under a convective CFL-like condition, by using a semi-implicit time discretisation algorithm. Finally, the correct asymptotic behaviour of the scheme in the limit of small Mach numbers is assessed on several academic test cases.