The paper is devoted to the convergence analysis of a well-known cell-centered Finite Volume Method (FVM) for a convection-difïusion problem in R. This FVM is based on Voronoi boxes and exponential fitting. To prove the convergence of the FVM, we use a new nonconforming PetrovGalerkin Finite Element Method (FEM) for which the System of linear équations coïncides completely with that of the FVM....

A simultaneous-approximation term is a non-reflecting boundary condition that usually accompanied by summation-by-parts schemes for provable time stability. While high-order convective flux based on reconstruction often employed in finite-volume method compressible turbulent flow, methods with the property involve either equally weighted averaging or second-order central fluxes. In present stud...

We develop a discretization scheme for the coupling of the finite volume method and the boundary element method in two dimensions, which describes, for example, the transport of a concentration in a fluid. The discrete system maintains naturally local conservation. In a bounded interior domain we approximate a diffusion convection reaction problem either by the finite volume element method or b...

sedimentation is one of the most important problems in harbors that results in considerable economic costs. harbor planforms affects the flow pattern in the harbor basin and consequently, plays an important role in sediment transport and sedimentation. in the present study, a two dimensional depth-averaged hydrodynamic and sediment transport model has been developed to investigate the effect of...

this paper introduces a mesh generating algorithm for solving the traffic flow equation as a conservation law equation. the idea behind the new method is to use the characteristic curves and moving non-oscillatory finite volume method. in addition, when characteristic curves intersect, the proposed scheme uses shock speed equation in order to improve computational efficiency. we also compare...

Finite-volume discretization schemes for viscous fluxes on general grids are compared using node-centered and cell-centered approaches. The grids range from regular grids to highly irregular grids, including random perturbations of the grid nodes. Accuracy and complexity are studied for four nominally second-order accurate schemes: a node-centered scheme and three cell-centered schemes (a node-...

Discretization of the viscous terms in current finite-volume unstructured-grid schemes are compared using node-centered and cell-centered approaches in two dimensions. Accuracy and efficiency are studied for six nominally second-order accurate schemes: a node-centered scheme, cell-centered node-averaging schemes with and without clipping, and cell-centered schemes with unweighted, weighted, and...

Cell-centered and node-centered approaches have been compared for unstructured finite-volume discretization of inviscid fluxes. The grids range from regular grids to irregular grids, including mixed-element grids and grids with random perturbations of nodes. Accuracy, complexity, and convergence rates of defect-correction iterations are studied for eight nominally second-order accurate schemes:...

We study the random choice method (RCM) for the Liouville equation of geometrical optics with discontinuous local wave speeds. This problem arises in the computation of high frequency waves through interfaces, where waves undergo partial transmissions and reflections. The numerical challenges include interface, contact discontinuities, and measurevalued solutions. The purpose of this paper is t...

Fluid flow through porous media is of great importance for many natural systems, such as transport of groundwater flow, pollution transport and mineral processing. In this paper, we propose and validate a novel finite volume formulation of the lattice Boltzmann method for porous flows, based on the Brinkman–Forchheimer equation. The porous media effect is incorporated as a force term in the lat...