The DFLU flux for systems of conservation laws

Adi Adimurthi (1) , G. D. Veerappa Gowda (1) , Jérôme Jaffré (2)

1 TIFR-CAM - Center for Applicable Mathematics [Bangalore]
2 POMDAPI - Environmental Modeling, Optimization and Programming Models

The DFLU numerical flux was introduced in order to solve hyperbolic scalar conservation laws with a flux function discontinuous in space. We show how this flux can be used to solve certain class of systems of conservation laws such as systems modeling polymer flooding in oil reservoir engineering. Furthermore, these results are extended to the case where the flux function is discontinuous in the space variable. Such a situation arises for example while dealing with oil reservoirs which are heterogeneous. Numerical experiments are presented to illustrate the efficiency of this new scheme compared to other standard schemes like upstream mobility, Lax-Friedrichs and Force schemes.

Mots clés: finite volumes; finite differences; Riemann solvers; system of conservation laws; flow in porous media; polymer flooding

Domaines: Analyse numérique [cs.NA]

Adi Adimurthi, G. D. Veerappa Gowda, Jérôme Jaffré. The DFLU flux for systems of conservation laws. Journal of Computational and Applied Mathematics, 2013, 247, pp.102-123. ⟨10.1016/j.cam.2012.12.025⟩. ⟨hal-00922936⟩