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A mathematical model of surface waves in a system of two porous layers
Wiryanto L.H.a, Djohan W.a
a Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Indonesia
[vc_row][vc_column][vc_row_inner][vc_column_inner][vc_separator css=”.vc_custom_1624529070653{padding-top: 30px !important;padding-bottom: 30px !important;}”][/vc_column_inner][/vc_row_inner][vc_row_inner layout=”boxed”][vc_column_inner width=”3/4″ css=”.vc_custom_1624695412187{border-right-width: 1px !important;border-right-color: #dddddd !important;border-right-style: solid !important;border-radius: 1px !important;}”][vc_empty_space][megatron_heading title=”Abstract” size=”size-sm” text_align=”text-left”][vc_column_text]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. © 2010 by IJAMAS, CESER Publications.[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Author keywords” size=”size-sm” text_align=”text-left”][vc_column_text]Damped waves,Darcy’s law,Dominant matrix,Finite difference equations,Gauss Seidel iteration,Nonlinear terms,Numerical solution,Porous layers,Porous medium,Potential function,System of equations,Taylor approximation,Time averages,Wave models[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Indexed keywords” size=”size-sm” text_align=”text-left”][vc_column_text]Darcy’s law,Diffusive type equation,Potential function,Two porous layers[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Funding details” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”DOI” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][/vc_column_inner][vc_column_inner width=”1/4″][vc_column_text]Widget Plumx[/vc_column_text][/vc_column_inner][/vc_row_inner][/vc_column][/vc_row][vc_row][vc_column][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][/vc_column][/vc_row]