In this paper we consider mixed finite element methods for second order elliptic problems. In the case of the lowest order Brezzi-Douglas-Marini elements （if d = 2） or Brezzi- Douglas-Duran-Fortin elements （if d = ...In this paper we consider mixed finite element methods for second order elliptic problems. In the case of the lowest order Brezzi-Douglas-Marini elements （if d = 2） or Brezzi- Douglas-Duran-Fortin elements （if d = 3） on rectangular parallelepipeds, we show that the mixed method system, by incorporating certain quadrature rules, can be written as a simple, cell-centered finite difference method. This leads to the solution of a sparse, positive semidefinite linear system for the scalar unknown. For a diagonal tensor coefficient, the sparsity pattern for the scalar unknown is a five point stencil if d = 2, and seven if d = 3. For a general tensor coefficient, it is a nine point stencil, and nineteen, respectively. Applications of the mixed method implementation as finite differences to nonisothermal multiphase, multicomponent flow in porous media are presented.展开更多
This paper is concerned with the numerical simulation of multiphase,multi-component flow in porous media.The model equations are based on compositional flow with mass interchange between phases.The compositional model...This paper is concerned with the numerical simulation of multiphase,multi-component flow in porous media.The model equations are based on compositional flow with mass interchange between phases.The compositional model consists of Darcy’s law for volumetric flow velocities,mass conservation for hydrocarbon components,ther-modynamic equilibrium for mass interchange between phases,and an equation of state for saturations.High-accurate finite volume methods on unstructured grids are used to discretize the model governing equations.Special emphasis is placed on studying the influence of gravitational effects on the overall displacement dynamics.In particular,free and forced convections,diffusions,and dispersions are studied in separate and com-bined cases,and their interplays are intensively analyzed for gravitational instabilities.Extensive numerical experiments are presented to validate the numerical study under consideration.展开更多
文摘In this paper we consider mixed finite element methods for second order elliptic problems. In the case of the lowest order Brezzi-Douglas-Marini elements （if d = 2） or Brezzi- Douglas-Duran-Fortin elements （if d = 3） on rectangular parallelepipeds, we show that the mixed method system, by incorporating certain quadrature rules, can be written as a simple, cell-centered finite difference method. This leads to the solution of a sparse, positive semidefinite linear system for the scalar unknown. For a diagonal tensor coefficient, the sparsity pattern for the scalar unknown is a five point stencil if d = 2, and seven if d = 3. For a general tensor coefficient, it is a nine point stencil, and nineteen, respectively. Applications of the mixed method implementation as finite differences to nonisothermal multiphase, multicomponent flow in porous media are presented.
文摘This paper is concerned with the numerical simulation of multiphase,multi-component flow in porous media.The model equations are based on compositional flow with mass interchange between phases.The compositional model consists of Darcy’s law for volumetric flow velocities,mass conservation for hydrocarbon components,ther-modynamic equilibrium for mass interchange between phases,and an equation of state for saturations.High-accurate finite volume methods on unstructured grids are used to discretize the model governing equations.Special emphasis is placed on studying the influence of gravitational effects on the overall displacement dynamics.In particular,free and forced convections,diffusions,and dispersions are studied in separate and com-bined cases,and their interplays are intensively analyzed for gravitational instabilities.Extensive numerical experiments are presented to validate the numerical study under consideration.
