An integral approach to compute compressible fluid flows in domains containing obstacles

Jean-Marc Hérard (1, 2) , Xavier Martin (1)

1 I2M - Institut de Mathématiques de Marseille
2 EDF R&D STEP - Simulation et Traitement de l'information pour l'Exploitation des systèmes de Production

We detail in this paper an integral approach in order to cope with the computation of flows of a compressible fluid in a physical domain containing many small obstacles. The basic methodology and the main ingredients used in schemes are provided, together with some exact solutions that are used to benchmark the integral approach. The latter is compared to the reference solution that accounts for all obstacles through standard wall-boundary conditions. Numerical results are also shown to be more accurate than the standard well-balanced approach. This work is actually the sequel of paper [1] that investigates the computation of compressible flows in variable cross-section ducts.

Mots clés: Finite volumes; Integral approach / Flows in obstructed media / Well-balanced approach / Entropy

Domaines: Mathématiques [math]; Mécanique des fluides [physics.class-ph]

Jean-Marc Hérard, Xavier Martin. An integral approach to compute compressible fluid flows in domains containing obstacles. International Journal on Finite Volumes, 2015, 12 (1), pp.1-39. ⟨hal-01166478v2⟩