On the modelling, linear stability, and numerical simulation for advection-diffusion-reaction in poroelastic media
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We perform the linear growth analysis for a new PDE-based model for poromechanical processes (formulated in mixed form using the solid deformation, fluid pressure, and total pressure) interacting with diffusing and reacting solutes in the medium. We find parameter regions that lead to interesting behaviour of the coupled system. These mutual dependences between deformation and diffusive patterns are of substantial relevance in the study of morphoelastic changes in biomaterials. We provide a set of computational examples in 2D and 3D that can be used to form a better understanding on how, and up to which extent, the deformations of the porous structure dictate the generation and suppression of spatial patterning dynamics, also related to the onset of mechanochemical waves.
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