Bidomain models are commonly used for studying and simulating electrophysiological waves in the cardiac tissue. Most of the time, the associated PDEs are solved using explicit finite difference methods on structured grids. We propose an implicit finite element method using unstructured grids for an anisotropic bidomain model. The impact and numerical requirements of unstructured grid methods is...

The objective of this work is to design explicit finite volumes schemes for specific systems of conservations laws with stiff source terms, which degenerate into diffusion equations. We propose a general framework to design an asymptotic preserving scheme, that is stable and consistent under a classical hyperbolic CFL condition in both hyperbolic and diffusive regime, for any two-dimensional un...

two-dimensional euler equations have been solved on an unstructured grid. an upwind finite volume scheme, based on roes flux difference splitting method, is used to discretize the equations. using advancing front method, an initial delaunay triangulation has been made. the adaptation procedure involves mesh enrichment coarsening in regions of flow with high low gradients of flow properties, acc...

This work presents a multidimensional cell-centered unstructured finite volume scheme for the solution of multimaterial compressible fluid flows written in the Lagrangian formalism. This formulation is considered in the Arbitrary-Lagrangian-Eulerian (ALE) framework with the constraint that the mesh and the fluid velocity coincide. The link between the vertex velocity and the fluid motion is obt...

A numerical model is presented for simulating shallow-water flows over dry and irregular bottom. The model is based on a projection method, which consists of combining the momentum and continuity equations in order to establish a Poisson-type equation for the water surface level. The computed domain is discretised by finite volumes on an unstructured grid. A 2nd-order upwind scheme coupled with...

CFD has become more and more used in the industry for the simulation of flows. Nevertheless, the complex configurations of real engineering problems make difficult the application of very accurate methods that only works on structured grids. From this point of view, the development of higher order methods for unstructured grids is desirable. The finite volume method can be used with unstructure...

It is announced that the Maxwell equations can be solved on unstructured grids using finite integration methods. Numerical experiments show that next to the finite-volume method, a discretization technique can be defined based on ’finite-surface’ integration.

Our objective is to analyse a commonly used edge based finite volume approximation of the Laplacian and construct an accurate and stable way to implement boundary conditions. Of particular interest are general unstructured grids where the strength of the finite volume method is fully utilised. As a model problem we consider the heat equation. We analyse the Cauchy problem in one and several spa...