In most structures with heterogeneities, such as porous media, the complexity of the geometry often prevents the computation of conservation laws at the smallest scales.
One way to model the system is to filter out the high-frequency fluctuations contained in the microscale details by averaging and adopt a homogenized description.
Obtaining the average equations directly from fundamental principles at the microscale can be performed using a number of mathematical approaches, including homogenization theories often based on multiscale asymptotics and the volume averaging theory.
For linear problems and locally periodic structures, these often yield very similar macroscale equations in which effective parameters, such as the permeability, can be calculated by solving closure problems in a unit-cell.
