We present different ways, coming from Finite Volume or Mixed Finite Element frameworks, to discretize convection terms in Hybrid Finite Volume, Mimetic Finite Difference and Mixed Finite Volume methods for elliptic equations. We compare them through several numerical tests, and we present an application to a system modeling miscible flows in porous media.

saccharomyces cerevisiae (baker’s yeast) can exhibit sustained oscillations during the operation in a continuous bioreactor that adversely affects its stability and productivity. because of heterogeneous nature of cell populations, the cell population balance equation (pbe) can be used to capture the dynamic behavior of such cultures. in this work, an unstructured-segregated model is used for d...

In this paper, we propose a novel family of semi-implicit hybrid finite volume/finite element schemes for computational fluid dynamics (CFD), in particular the approximate solution incompressible and compressible Navier-Stokes equations, as well shallow water equations on staggered unstructured meshes two three space dimensions. The key features method are use an edge-based/face-based dual mesh...

unsteady flow through non - homogeneous and anisotropic porous media can be modeled by a partial differential equation.' this-equation cannot be solved analytically. hence, numerical methods. such as the finite element and the finite difference methods might be employed. in this study a mathematical model has been developed using the fully implicit finite difference method with control vol...

We propose two algorithms of two-level methods for resolving the nonlinearity in the stabilized finite volume approximation of the Navier-Stokes equations describing the equilibrium flow of a viscous, incompressible fluid. A macroelement condition is introduced for constructing the local stabilized finite volume element formulation. Moreover the two-level methods consist of solving a small nonl...

A parallel solvers package of three solvers with a unified user interface is developed for solving a range of sparse symmetric complex linear systems arising from disc~tization of partial differential equations based on unstructu~d meshs using finite element, finite difference and finite volume analysis. Once the data interface is set up, the package constructs the sparse symmetric complex matr...

We show how a stable and accurate hybrid procedure for fluid flow can be constructed. Two separate solvers, one using high order finite difference methods and another using the node-centered unstructured finite volume method are coupled in a truly stable way. The two flow solvers run independently and receive and send information from each other by using a third coupling code. Exact solutions t...

This paper, which is largely the fruit of an invited talk on the topic at the latest International Conference on Coastal Engineering, describes the state of the art of modelling by means of Boussinesq-type models (BTMs). Motivations for using BTMs as well as their fundamentals are illustrated, with special attention to the interplay between the physics to be described, the chosen model equation...