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Convective stability of CO\(_2\) sequestration in a porous medium. (English) Zbl 07446961

Summary: We considered an incompressible fluid-saturated porous layer bounded by two infinite parallel plates. The Boussinesq approximation and Darcy’s law are applied. The permeability is assumed to be a linear function of the depth \(z\). The linear stability is investigated. The long wavelength expansion method is applied to conduct the weakly nonlinear stability analysis. The evolution equation is derived and analyzed. A uniformly valid periodic solution of the evolution equation is obtained by the application of the Poincaré-Lindstedt method. Some numerical simulations are presented.

MSC:

76E20 Stability and instability of geophysical and astrophysical flows
76E15 Absolute and convective instability and stability in hydrodynamic stability
76S05 Flows in porous media; filtration; seepage
76-10 Mathematical modeling or simulation for problems pertaining to fluid mechanics
76E06 Convection in hydrodynamic stability
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