In this work, we discuss a family of finite element discretizations for the incompressible Stokes problem using continuous pressure approximations on simplicial meshes. We show that after a simple and cheap correction, the mass-fluxes obtained by the considered schemes preserve local conservation on dual cells without reducing the convergence order. This allows the direct coupling to vertex-cen...

A new face-centred finite volume method (FCFV) for Stokes problems involving sharp interfaces is proposed. Two formulations, based on two strong forms of the problem, and using different mixed variables, are presented. Particular attention paid to symmetry resulting system global equations, a simple rewriting interface boundary condition proposed ensure that one formulations preserves linear us...

In this paper, we present a conservative cell-centered Lagrangian Finite Volume scheme for solving the hyperelasticity equations on unstructured multidimensional grids. The starting point of approach is FV discretization named EUCCLHYD and introduced in context hydrodynamics. Here, it combined with posteriori Multidimensional Optimal Order Detection (MOOD) limiting strategy to ensure robustness...

In this paper, we propose an efficient quadratic interpolation formula utilizing solution gradients computed and stored at nodes demonstrate its application to a third-order cell-centered finite-volume discretization on tetrahedral grids. The proposed is constructed based of computing projected derivative. It in that it completely eliminates the need compute store second derivatives variables o...

To improve the calculation of the flow properties of an aerospike nozzle, different turbulence models were investigated in this study. The primary shape of the nozzle plug is determined through utilizing an approximate method. The flow field is, then, simulated using the Navier-Stokes equations for compressible flows. The commercial computational fluid dynamics code Fluent is used to simulate t...

We present a finite volume method based on the integration of the Laplace equation on both the cells of a primal almost arbitrary two-dimensional mesh and those of a dual mesh obtained by joining the centers of the cells of the primal mesh. The key ingredient is the definition of discrete gradient and divergence operators verifying a discrete Green formula. This method generalizes an existing f...

The goal of this study is to apply the MUSCL scheme to the linear advection equation on general unstructured grids and to examine the eigenvalue stability of the resulting linear semi-discrete equation. Although this semi-discrete scheme is in general stable on cartesian grids, numerical calculations of spectra show that this can sometimes fail for generalizations of the MUSCL method to unstruc...

Models applied in image processing are often described by nonlinear PDEs in which a good approximation of gradient plays an important role especially in such cases where irregular finite volume grids are used. In image processing, such a situation can occur during a coarsening based on quadtree grids. We present a construction of a deformed quadtree grid in which the connection of representativ...

We study the consistency and convergence of the cell-centered Finite Volume (FV) external approximation of H 0 (Ω), where a 2D polygonal domain Ω is discretized by a mesh of convex quadrilaterals. The discrete FV derivatives are defined by using the so-called Taylor Series Expansion Scheme (TSES). By introducing the Finite Difference (FD) space associated with the FV space, and comparing the FV...