A Control Volume Finite Element Method for Local Mesh Refinement

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Abstract
This paper describes a control volume-finite element technique for coupling coarse grids with local fine meshes. The pressure is treated in a finite element manner, while the mobility terms are upstream weighted in the usual way. This requires identification of the cell volumes and edges which are consistent with the linear finite element discretization of the pressure. In order to ensure that the pressure equation yields an M-matrix, various conditions are required for the type of triangulation allowed. Since the form of the equations is similar to the usual finite difference discretization, standard techniques can be used to solve the Jacobian. The local mesh refinement method is demonstrated on some thermal reservoir simulation problems, and computational results presented. Significant savings in execution times are obtained while giving similar predictions to global fine mesh runs.

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