Finite Volume Discretization of Flow in Porous Media by the MATLAB System

In this paper, a finite volume scheme is used to discretize flow in porous media. A numerical method for treating advection-dominated contaminant transport for flow of groundwater is described. This system combines the advantages of numerical discretization and the finite volume method (like local mass conservation). The equations are discretized using a finite volume approach. The resulting nonlinear differential system is integrated in time using a solver. The conservation of energy (convection-diffusion) equation is solved using a special method for reducing the oscillations induced by the standard finite volume method. Consequently, a mathematical model for multi-component flow transport in an anisotropic media is presented, which couples the equations for multi-component diffusion and Darcy's law for flow in a porous medium. Furthermore, application of an integrated matlab system in several studies has been provided. The integrated matlab system is based on open data formats and standards and may be used for many other application areas, especially where modeling in 2D and 3D is involved. Numerical simulations are performed to validate the model and investigate the effect. The final purpose of this paper is to discuss and compare the difference between the finite volume scheme for uniform and for unstructured grids, which is shown to be less than 0.2 percent.