Premium
A combined finite volumes ‐ finite elements method for a low‐Mach model
Author(s) -
Calgaro Caterina,
Colin Claire,
Creusé Emmanuel
Publication year - 2019
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4706
Subject(s) - finite volume method , finite element method , pressure correction method , mathematics , mach number , compressibility , projection method , convergence (economics) , ideal gas , conservation of mass , flow (mathematics) , mathematical analysis , mechanics , physics , mathematical optimization , geometry , dykstra's projection algorithm , thermodynamics , economics , economic growth
Summary In this paper, we develop a finite volumes ‐ finite elements method based on a time splitting to simulate some low‐Mach flows. The mass conservation equation is solved by a vertex‐based finite volume scheme using a τ ‐limiter. The momentum equation associated with the compressibility constraint is solved by a finite element projection scheme. The originality of the approach is twofold. First, the state equation linking the temperature, the density, and the thermodynamic pressure is imposed implicitly. Second, the proposed combined scheme preserves the constant states, in the same way as a similar one previously developed for the variable density Navier‐Stokes system. Some numerical tests are performed to exhibit the efficiency of the scheme. On the one hand, academic tests illustrate the ability of the scheme in term of convergence rates in time and space. On the other hand, our results are compared to some of the literature by simulating a transient injection flow as well as a natural convection flow in a cavity.