We present Finite Volume methods for diffusion equations on generic meshes, that received
important coverage in the last decade or so. After introducing the main ideas and …

We propose a cell-centered finite volume (FV) scheme with the minimal stencil formed by the
closest neighbouring cells. The discrete solution satisfies the discrete maximum principle …

We present a new nonlinear monotone finite volume method for diffusion equation and its
application to two-phase flow model. We consider full anisotropic discontinuous diffusion or …

Platelets upregulate the generation of thrombin and reinforce the fibrin clot which increases
the incidence risk of venous thromboembolism (VTE). However, the role of platelets in the …

We present in this article a positive finite volume method for diffusion equation on deformed
meshes. This method is mainly inspired from, and uses auxiliary unknowns at the nodes of …

We consider the solution of systems of nonlinear algebraic equations that appear in a
positivity preserving finite volume scheme for steady-state advection-diffusion equations. We …

The paper develops a hybrid method for solving a system of advection–diffusion equations
in a bulk domain coupled to advection–diffusion equations on an embedded surface. A …

We present a novel cell-centered finite volume discretization of the heterogeneous and
anisotropic diffusion problems on polygonal meshes. The unknowns of the resulting linear …

While many numerical methods for the linear transport equation are available in the
literature in 1D or on Cartesian meshes, fewer works are dedicated to the resolution of this …

Richards's equation describes steady-state or transient flow in a variably saturated medium.
For a medium having multiple layers of soils that are not aligned with coordinate axes, a …