A non-isodimensional finite-element approach to the modeling of transient flow and mass transport through domains with thin layers

A new finite element method (FEM) is developed for transient flow problems in multiple-scale media. Double or multiple nodes are used to model thin layers, or any set of 1D regions, as a discontinuity of variables and transform their effects into a body load acting at the interface with the rest of the domain. The formulation, called Multiple-Node FEM, offers two advantages. First, it removes the need for meshing and numerical integration along the thin direction and reduces the number of degrees of freedom. Second, it provides the basis for a non-isodimensional FEM which seamlessly combines domains with different dimensions.