One-dimensional transport element

The discrete form of the differential equation for mass transport for a one-dimensional transport element is


where is a vector containing the nodal values of the capillary pressure, is the conductivity matrix, is the capacity matrix and is the nodal flow rate vector ().

The capacity matrix is


where $ c$ is the capacity of the material, l is the length of the transport element and is the cross-sectional area of the transport element.

The conductivity matrix is defined as


Borek Patzak