Related papers: Second-order accurate finite volume method for wel…
In this paper, a second-order accurate method was developed for calculating fluid flows in complex geometries. This method uses cut-Cartesian cell mesh in finite volume framework. Calculus is employed to relate fluxes and gradients along…
Two finite volume methods are derived and applied to the solution of problems of incompressible flow. In particular, external inviscid flows and boundary-layer flows are examined. The firstmethod analyzed is a cell-centered finite volume…
A well-balanced second-order finite volume scheme is proposed and analyzed for a 2 X 2 system of non-linear partial differential equations which describes the dynamics of growing sandpiles created by a vertical source on a flat, bounded…
This paper presents a finite volume method for simulating two-phase flows using a level set approach coupled with volume of fluid method capable of simulating sharp fluid interfaces. The efficiency of the method is a result of the fact that…
Numerous infinite dimensional dynamical systems arising in different fields have been shown to exhibit a gradient flow structure in the Wasserstein space. We construct Two Point Flux Approximation Finite Volume schemes discretizing such…
We consider two-level finite element discretization methods for the stream function formulation of the Navier-Stokes equations. The two-level method consists of solving a small nonlinear system on the coarse mesh, then solving a linear…
We study a one dimensional model for two-phase flows in heterogeneous media, in which the capillary pressure functions can be discontinuous with respect to space. We first give a model, leading to a system of degenerated non-linear…
We investigate the performance of the finite volume method in solving viscoplastic flows. The creeping square lid-driven cavity flow of a Bingham plastic is chosen as the test case and the constitutive equation is regularised as proposed by…
In this work we are interested in dealing with single-phase flows in fractured porous media for underground processes. We focus our attention on domains where the presence of faults, with thickness several orders of magnitude smaller than…
We consider the numerical approximation of single phase flow in porous media by a mixed finite element method with mass lumping. Our work extends previous results of Wheeler and Yotov, who showed that mass lumping together with an…
We extend our recent work on the creeping flow of a Bingham fluid in a lid-driven cavity, to the study of inertial effects, using a finite volume method and the Papanastasiou regularisation of the Bingham constitutive model [J. Rheology 31…
Conventional mathematical models for simulating incompressible fluid flow problems are based on the Navier-Stokes equations expressed in terms of pressure and velocity. In this context, pressure-velocity coupling is a key issue, and…
We propose a new unstructured numerical subgrid method for solving the shallow water equations using a finite volume method with enhanced bathymetry resolution. The method employs an unstructured triangular mesh with support for…
We propose a simple modification of standard WENO finite volume methods for Cartesian grids, which retains the full spatial order of accuracy of the one-dimensional discretization when applied to nonlinear multidimensional systems of…
Finite-volume numerical method for study shallow water flows over an arbitrary bed profile in the presence of external force is proposed. This method uses the quasi-two-layer model of hydrodynamic flows over a stepwise boundary with…
We propose a two-point flux approximation finite-volume scheme for a stochastic non-linear parabolic equation with a multiplicative noise. The time discretization is implicit except for the stochastic noise term in order to be compatible…
A second-order face-centred finite volume strategy on general meshes is proposed. The method uses a mixed formulation in which a constant approximation of the unknown is computed on the faces of the mesh. Such information is then used to…
We consider the depth-integrated non-hydrostatic system derived by Yamazaki et al. An efficient formally second-order well-balanced hybrid finite volume finite difference numerical scheme is proposed. The scheme consists of a two-step…
The Finite Volume Method in Computational Fluid Dynamics to numerically model a fluid flow problem involves the process of formulating the numerical flux at the faces of the control volume. This process is important in deciding the…
In this article, we analyze a two-level finite element method for the equations of motion arising in the flow of 2D Oldroyd model with non-smooth initial data. It involves solving the non-linear problem on a coarse grid of mesh-size $H$ and…