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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 |

### Keywords:

stability analysis; long wavelength method; Poincaré-Lindstedt method; periodic solution; carbon sequestration
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\textit{M. H. DarAssi}, Nonlinear Dyn. Syst. Theory 21, No. 2, 179--192 (2021; Zbl 07446961)

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