A Finite Element Solver for the Advection Equation Applied to Interface Tracking.

A numerical strategy for the finite element simulation of the flow of two immiscible fluids has been developed based on unstructured triangular meshes. The tracking of the interface between the two fluids is accomplished by means of an advection equation for the volume fraction of one of these fluids. An accurate description of the interface is achieved by means of an automatic mesh refinement procedure developed for the simulation of fluid flow in twin-screw extruders. The advantage of this technique comes from the use of one single reference mesh. At each time iteration, this reference mesh is adapted by splitting up the elements in the vicinity of the interface into sub-elements. Local refinement can then be carried out with one single mesh to be generated before the simulation is started. First, the method will be presented in detail. It will then be applied to two-dimensional classical benchmark problems: the advection skew to the mesh and the transport of a square. © 2004 American Institute of Physics [ABSTRACT FROM AUTHOR]