Stochastic porous media, towards a digital meniscus*

Flow and transport computations for explicit microstructures of stochastic porous media, here the knee meniscus, are prohibitively time consuming. First, as the porous microstructure is geometrically complex, each simulation is considerably time consuming. Second, the porous microstructure is intrinsically stochastic as it varies from location to location and from specimen to specimen, requiring numerous experiments and flow computations to be performed. First, we address the continuum biological hydrodynamics simulation in complex geometries, by presenting a novel integrated computational approach using the Discretisation-Corrected Particle Strength Exchange (DC PSE) operator [1] discretisation in a mesh-less solver, the solver is coupled with Brinkman penalisation [2] to add a layer of robustness when dealing with complex geometries. Steady and unsteady Navier-Stokes equations are solved using the solver. Secondly, we introduce a data driven framework in which the porous microstructures are homogenised to enable simulations in which the explicit microstructural representation is omitted, but the stochastic transport characteristics are preserved. Only a few meniscuses need to be characterised and a few sub- scale microstructural simulations on statistical volume elements are required to probabilistically identify the parameters of the random spatial fields of the permeability coefficient. The probabilistic identifica- tion setting assumes that each spatial input field is a realisation from a single, joint multi-dimensional probability density function. The probabilistic identification setting is based on Bayes' theorem, which only requires a limited number of measurements. Finally, we will use the identified probability density function to rapidly propagate the uncertainty with the fast homogenised model.