Comparison of finite difference and finite volume methods for numerical simulation of filtration in a cylindrical porous filter
Abstract
This study presents a comparative numerical investigation of the Finite Difference Method (FDM) and the Finite Volume Method (FVM) for simulating filtration processes in a cylindrical porous filter. The mathematical model combines axisymmetric Brinkman–Darcy flow equations with advection–diffusion–reaction equations describing the transport of dissolved substances in a porous medium. Both numerical methods are applied to the same mathematical model under identical initial, boundary, and computational conditions. The comparison considers pressure and velocity distributions, solute concentration, numerical accuracy, grid convergence, conservation properties, stability, and computational efficiency. Numerical experiments are performed to evaluate the influence of the computational method on the simulation results. The results demonstrate the advantages and differences of the finite difference and finite volume approaches and provide a basis for selecting an appropriate numerical method for modeling filtration processes in cylindrical porous media.