We study a time implicit Finite Volume scheme for degenerate Cahn–Hilliard model proposed in [W. E and P. Palffy-Muhoray, Phys. Rev. 55 (1997) R3844–R3846] studied mathematically by the authors [C. Cancès, D. Matthes F. Nabet, Arch. Ration. Mech. Anal. 233 (2019) 837–866]. The is shown to preserve key properties of continuous model, namely mass conservation, positivity concentrations, decay ene...

Finite volume (FV) numerical solvers of the two-dimensional shallow water equations are core to industry-standard flood models. The second-order Discontinuous Galerkin (DG2) alternative, although a viable way forward improve current FV-based models, is yet under-studied and rarely used support modelling applications. This paper systematically explores compares predictive properties robust DG2 m...

We present in this paper a pressure correction scheme for the drift-flux model combining finite element and finite volume discretizations, which is shown to enjoy essential stability features of the continuous problem: the scheme is conservative, the unknowns are kept within their physical bounds and, in the homogeneous case (i.e. when the drift velocity vanishes), the discrete entropy of the s...

We present in this paper a pressure correction scheme for the drift-flux model combining finite element and finite volume discretizations, which is shown to enjoy essential stability features of the continuous problem: the scheme is conservative, the unknowns are kept within their physical bounds and, in the homogeneous case (i.e. when the drift velocity vanishes), the discrete entropy of the s...

Numerical solutions based on standard finite volume method are presented for the study of heat transfer and fluid dynamic characteristics in turbulent flows behind a single sided backward-facing step. The calculation of the differential equations is performed using SIMPLE algorithm. For the turbulent quantities standard K-model is used. Predicted mean velocity profiles and reattachment lengths ...

Reservoir formations exhibit a wide range of heterogeneity from micro to macro scales. A simulation that involves all of these data is highly time consuming or almost impossible; hence, a new method is needed to meet the computational cost. Moreover, the deformations of the reservoir are important not only to protect the uppermost equipment but also to simulate fluid pattern and petroleum produ...

We define a combined edge FV-FE scheme for a bone healing model. This choice of discretization allows to take into account anisotropic diffusions and does not impose any restrictions on the mesh. Moreover, following [3], we propose a nonlinear correction to obtain a monotone scheme. We present some numerical experiments which show its good behavior.

In this paper a sequential coupling of mixed finite element and shock-capturing finite volume techniques is proposed, in order to numerically solve the system of partial differential equations arising from the Black-Oil model. The Brezzi–Douglas–Marini space of degree one (BDM1) is used to approximate the Darcy’s velocity in the parabolic-type pressure equation, while the system of mass conserv...