In this paper, we present a discrete duality finite volume (DDFV) method for 2-D flow problems in nonhomogeneous anisotropic porous media under diverse boundary conditions. We use the discrete gradient defined in diam...In this paper, we present a discrete duality finite volume (DDFV) method for 2-D flow problems in nonhomogeneous anisotropic porous media under diverse boundary conditions. We use the discrete gradient defined in diamond cells to compute the fluxes. We focus on the case of Dirichlet, full Neumann and periodic boundary conditions. Taking into account the periodicity is the main new ingredient with respect to our recent works. We explain the procedures step by step, for numerical solutions. We develop a matlab code for algebraic equations. Numerical tests were provided to confirm our theoretical results.展开更多
This paper presents and analyzes a Discrete Duality Finite Volume(DDFV)method to solve 2D diffusion problems under prescribed Robin boundary conditions.The derivation of a symmetric discrete problem is established.The...This paper presents and analyzes a Discrete Duality Finite Volume(DDFV)method to solve 2D diffusion problems under prescribed Robin boundary conditions.The derivation of a symmetric discrete problem is established.The existence and uniqueness of a solution to this discrete problem are shown via the positive definiteness of its associated matrix.We show that the discrete scheme meets the Neumann problem when the parameterα→0(and,in a sense,whenα→∞the Dirichlet problem).This work is a continuation of our work regarding the development of DDFV methods.The main innovation here is taking into account Robin’s boundary conditions.We provide a few steps of Matlab implementation and numerical tests to confirm the effectiveness of the method.展开更多
文摘In this paper, we present a discrete duality finite volume (DDFV) method for 2-D flow problems in nonhomogeneous anisotropic porous media under diverse boundary conditions. We use the discrete gradient defined in diamond cells to compute the fluxes. We focus on the case of Dirichlet, full Neumann and periodic boundary conditions. Taking into account the periodicity is the main new ingredient with respect to our recent works. We explain the procedures step by step, for numerical solutions. We develop a matlab code for algebraic equations. Numerical tests were provided to confirm our theoretical results.
文摘This paper presents and analyzes a Discrete Duality Finite Volume(DDFV)method to solve 2D diffusion problems under prescribed Robin boundary conditions.The derivation of a symmetric discrete problem is established.The existence and uniqueness of a solution to this discrete problem are shown via the positive definiteness of its associated matrix.We show that the discrete scheme meets the Neumann problem when the parameterα→0(and,in a sense,whenα→∞the Dirichlet problem).This work is a continuation of our work regarding the development of DDFV methods.The main innovation here is taking into account Robin’s boundary conditions.We provide a few steps of Matlab implementation and numerical tests to confirm the effectiveness of the method.
