Destruction of the family of steady states in the planar problem of Darcy convection

TL;DR

This paper investigates how perturbations in boundary conditions destroy the continuous family of steady states in Darcy convection within porous media, revealing transitions to limit cycles or isolated patterns through computational experiments.

Contribution

It demonstrates the destruction mechanisms of steady states in Darcy convection caused by boundary condition violations using a mimetic finite-difference approach.

Findings

Boundary condition violations lead to limit cycles or isolated convective patterns.

Different perturbations produce distinct transition scenarios.

The study provides computational insights into the stability of steady states.

Abstract

The natural convection of incompressible fluid in a porous medium causes for some boundary conditions a strong non-uniqueness in the form of a continuous family of steady states. We are interested in the situation when these boundary conditions are violated. The resulting destruction of the family of steady states is studied via computer experiments based on a mimetic finite-difference approach. Convection in a rectangular enclosure is considered under different perturbations of boundary conditions (heat sources, infiltration). Two scenario of the family of equilibria are found: the transformation to a limit cycle and the formation of isolated convective patterns.