A combined Finite Volumes -Finite Elements method for a low-Mach model: Application to the simulation of a transient injection flow

Caterina Calgaro (1, 2) , Claire Colin (1, 2) , Emmanuel Creusé (1, 2)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 RAPSODI - Reliable numerical approximations of dissipative systems

In this paper, we develop a combined 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 thermo-dynamic 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 on the scheme. On 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.

Mots clés: Low-Mach model; Finite Volume method; Finite Element method; Projection scheme

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]; Mécanique des fluides [physics.class-ph]

Caterina Calgaro, Claire Colin, Emmanuel Creusé. A combined Finite Volumes -Finite Elements method for a low-Mach model: Application to the simulation of a transient injection flow. 2017. ⟨hal-01574894v1⟩