A Mathematical Model of Surface Waves in a System of Two Porous Layers
Leo Hari Wiryanto, Warsoma Djohan · International Journal of Applied Mathematics & Statistics/International journal of applied mathematics and statistics · 2010
Surface waves in porous medium are modeled in this paper. A fluid occupying pore in a system of two porous layers with different characteristics, porosity and permeability, is disturbed such that the waves propagate on the surface. We derive the model in a diffusive type equation. The model is then solved numerically by a finite difference method, based on forward-time average centered-space. Taylor approximation is applied to the nonlinear term of the equation to obtain the finite difference equations in a diagonal dominant matrix, so that Gauss-Seidel iteration can be used to solve the system of equations, and numerical solutions for different character of the porous layers are obtained. Over-damped waves are performed in this paper. When both layers are given the same porosity and permeability, our result agrees to the wave model in one porous layer.