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Control-Volume Mixed Finite Element Methods

A key ingredient in simulation of flow in porous media is accurate determination of the velocities that drive the flow. Large-scale irregularities of the geology (faults, fractures and layers) suggest the use of irregular grids in simulation. This paper presents a control-volume mixed finite element method that provides a simple, systematic, easily implemented procedure for obtaining accurate velocity approximations on irregular block-centered grids. The control-volume formulation of Darcy's law can be viewed as a discretization into element-sized tanks with imposed pressures at the ends, giving a local discrete Darcy law analogous to the block-by-block conservation in the usual mixed discretization of the mass-conservation equation. Numerical results in two dimensions show second-order convergence in the velocity, even with discontinuous anisotropic permeability on an irregular grid. The method extends readily to three dimensions.

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  • "A key ingredient in simulation of flow in porous media is accurate determination of the velocities that drive the flow. Large-scale irregularities of the geology (faults, fractures and layers) suggest the use of irregular grids in simulation. This paper presents a control-volume mixed finite element method that provides a simple, systematic, easily implemented procedure for obtaining accurate velocity approximations on irregular block-centered grids. The control-volume formulation of Darcy's law can be viewed as a discretization into element-sized tanks with imposed pressures at the ends, giving a local discrete Darcy law analogous to the block-by-block conservation in the usual mixed discretization of the mass-conservation equation. Numerical results in two dimensions show second-order convergence in the velocity, even with discontinuous anisotropic permeability on an irregular grid. The method extends readily to three dimensions."@en
  • "Abstract: "A key ingredient in simulation of flow in porous media is accurate determination of the velocities that drive the flow. Large-scale irregularities of the geology (faults, fractures, and layers) suggest the use of irregular grids in simulation. This paper presents a control-volume mixed finite element method that provides a simple, systematic, easily implemented procedure for obtaining accurate velocity approximations on irregular block-centered grids. The control-volume formulation of Darcy's law can be viewed as a discretization into element-sized 'tanks' with imposed pressures at the ends, giving a local discrete Darcy law analogous to the block-by-block conservation in the usual mixed discretization of the mass-conservation equation. Numerical results in two dimensions show second-order convergence in the velocity, even with discontinuous anisotropic permeability on an irregular grid. The method extends readily to three dimensions.""@en

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  • "Control-Volume Mixed Finite Element Methods"@en
  • "Control-volume mixed finite element methods"@en

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