Multiscale modelling approaches for simulating transport phenomena in heterogeneous porous media

Multiscale models for simulating transport in porous media generally involve either upscaling techniques such as computational homogenisation, or the use of a distributed microstructure model. In the former, calculations on a representative 'mirocell' are used to derive effective coefficients for use in the macroscopic averaged equations, while in the latter coupled continuum equations are solved simultaneously at the macro and micro scales. In this talk, an overview will be provided of the computational techniques employed to solve the nonlinear conservation laws at the macroscale and the numerical methods used for simulating the potentially anomalous transport phenomena evident at the microscale. It is thought that these phenomena are driven by the constrained interactions arising within the complex and non-homogeneous microstructures evident at the pore scale. We will investigate the use of generalised transport equations based on fractional operators to model such phenomena because they have the unique ability to describe memory and non-local behaviour. Results are exhibited for the drying of lignocelluosic materials such as wood.