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A Mathematical Model of Surface Waves in a System of Two Porous Layers

L. H. Wiryanto, W. Djohan

Abstract


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.

Keywords


Two porous layers, diffusive type equation, Darcy’s law, potential function

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