TITLE:
Numerical Solution of 2-D Diffusion Problems Using Discrete Duality Finite Volume Method on General Boundary Conditions
AUTHORS:
Hubert Donfack, Aubin Kinfack Jeutsa
KEYWORDS:
Flow Problems, Nonhomogeneous Anisotropic Media, Finite Volumes, Test Simulations
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.10 No.6,
June
28,
2022
ABSTRACT: 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.