Finite volume schemes for diffusion equations: introduction to and review of modern methods
J Droniou - Mathematical Models and Methods in Applied …, 2014 - World Scientific
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 …
important coverage in the last decade or so. After introducing the main ideas and …
Minimal stencil finite volume scheme with the discrete maximum principle
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 …
closest neighbouring cells. The discrete solution satisfies the discrete maximum principle …
A mathematical model to quantify the effects of platelet count, shear rate, and injury size on the initiation of blood coagulation under venous flow conditions
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 …
the incidence risk of venous thromboembolism (VTE). However, the role of platelets in the …
A monotone nonlinear finite volume method for diffusion equations and multiphase flows
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 …
application to two-phase flow model. We consider full anisotropic discontinuous diffusion or …
A positive scheme for diffusion problems on deformed meshes
X Blanc, E Labourasse - ZAMM‐Journal of Applied …, 2016 - Wiley Online Library
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 …
meshes. This method is mainly inspired from, and uses auxiliary unknowns at the nodes of …
Anderson acceleration for nonlinear finite volume scheme for advection-diffusion problems
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 …
positivity preserving finite volume scheme for steady-state advection-diffusion equations. We …
An interpolation-free cell-centered discretization of the heterogeneous and anisotropic diffusion problems on polygonal meshes
S Miao, J Wu, Y Yao - Computers & Mathematics with Applications, 2023 - Elsevier
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 …
anisotropic diffusion problems on polygonal meshes. The unknowns of the resulting linear …
A hybrid finite volume–finite element method for bulk–surface coupled problems
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 …
in a bulk domain coupled to advection–diffusion equations on an embedded surface. A …
An asymptotic preserving method for the linear transport equation on general meshes
P Anguill, P Cargo, C Énaux, P Hoch… - Journal of …, 2022 - Elsevier
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 …
literature in 1D or on Cartesian meshes, fewer works are dedicated to the resolution of this …
Second-order accurate finite volume schemes with the discrete maximum principle for solving Richards' equation on unstructured meshes
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 …
For a medium having multiple layers of soils that are not aligned with coordinate axes, a …