María González Taboada

Departamento de Matemáticas & CITIC (Universidade da Coruña, UDC)

Título: Flow in a Moving Poroelastic Medium: Fully Discrete Analysis and Simulations

Resumen: Many natural and biological materials are porous and deformable: soils, biological tissues, hydrogels or cartilage. In these materials, fluid flows inside a solid skeleton that can also move. When both the fluid and the solid move simultaneously - even slowly - predicting the behaviour of the system becomes surprisingly difficult.

In this work we study a mathematical model describing a fluid flowing through an elastic porous solid that is itself in motion. Although the equations are linearised, they remain strongly coupled because the fluid and the solid velocities influence each other. This creates important challenges for both analysis and numerical simulation.

We present two computational methods to approximate the solution of the model: a first-order time discretisation (Backward Euler) and a second-order one (BDF2). We explain how to design stable finite element schemes and how to estimate the numerical error produced by the simulations.

The talk will emphasise the intuition behind the model, the difficulties caused by coupling multiple physical processes, and how mathematical analysis guarantees that the numerical simulations are reliable. Numerical experiments illustrate how the methods behave in practice.