A cell-centered Lagrangian-mesh diffusion differencing scheme

A Finite Volume Method for the Approximation of Diffusion Operators on Distorted Meshes

“…When the mesh is made up of arbitrary quadrangles we obtain a nine-point method which can be compared with the quadrilateral finite element method and the methods described in [2,5,8,13], although the degrees of freedom are not the same.…”

“…In order to satisfy this condition several methods have already been proposed [2,5,8,13]. Here we present a new finite volume method which has been briefly described in [7].…”

Combining Cell- and Point-Centered Methods in 3D, Unstructured-Grid Radiation–Hydrodynamic Codes

“…For example, Morel et al [6] propose a cell-centered diffusion scheme (MDHW) for quadrilateral (logically orthogonal) grids which has two advantages over the K&P schemes: (1) If u is linear, the discretization of ∇ · ∇u does vanish and (2) the solution seems to converge with secondorder accuracy, regardless of the smoothness of the mesh. However, MDHW has the following disadvantages: (1) In addition to the cell-centered unknowns, edge-centered unknowns are introduced which triples the size of the linear system.…”

Differencing the diffusion equation on unstructured meshes in 2-D

“…Conversely, development of unstructured rncsh diffusion methods lias been lacking. While Morel 4 , Kershaw 5 , Slicslakov" and others have done a great deal of work on diffusion schemes for logically-rectangular grids, to our knowledge there has been no work on discretizations of the diffusion equation on unstructured rneshes of polygons.…”