Relaxation properties of a 1D flow through a porous material without and with adsorption
- Albers, Bettina
- Wilmański, Krzysztof
2010 Mathematics Subject Classification
- 76S05 76E20 74J05
- flows in porous media, stability of geophysical flows, linear waves
In this paper we investigate relaxation properties of a 1D steady state flow in a porous medium which is linearly perturbed in flow direction. We consider two cases of relaxation: without adsorption and with adsorption. The fields are assumed to be a superposition of a stationary (nonuniform) solution and of infinitesimal disturbances in the form of a linear wave ansatz. We show that such flows are absolutely stable with respect to longitudinal disturbances. It means that a smaller real part of the exponent in this ansatz yields a faster relaxation of the perturbation and the flow recovers faster the equilibrium. We solve numerically the eigenvalue problem for the first step field equations using a finite difference scheme and compare the results for the perturbation without mass exchange with the analytical solution. Calculations demonstrate the range of permeability coefficients with the fastest relaxation and the fastest convergence of numerical solutions.