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Center for Nonlinear Studies |
We present a new cell-centered diffusion scheme on unstructured mesh. The main feature of this scheme lies in the introduction of two half normal fluxes and two temperatures on each edge. A local variational formulation written for each corner cell provides the discretization of the half normal fluxes. This discretization yields a linear relation between the half normal fluxes and the temperatures defined on the two edges impinging on a node. The continuity of the half normal fluxes written for each edge around a node leads to a linear system. Its resolution enables to eliminate locally the edge temperatures in function of the mean temperature in each cell. By this way, we obtain a small symmetric positive definite matrix located at each node. Finally, by summing all the nodal contribution, one gets a linear system satisfied by the cell-centered unknowns. This system is characterized by a symmetric positive definite matrix. We show numerical results on various test cases which exhibit the good behavior of this new scheme. First, it preserves the linear solutions on triangular mesh. It reduces to a classical five points scheme on rectangular grids. For non-orthogonal quadrangular grids we obtain an accuracy which is almost second order on smooth meshes.
Host: Mikhail Shashkov