ENHANCED-DISCRETIZATION INTERFACE-CAPTURING TECHNIQUE (EDICT) FOR COMPUTATION OF UNSTEADY FLOWS WITH INTERFACES

We present the Enhanced-Discretization Interface-Capturing Technique ( EDICT) for computation of unsteady flow problems with interfaces, such as two-fluid and free-surface flows. In EDICT, we solve, over a non-m oving mesh, the Navier-Stokes equations together with an advection equ ation governing the evolution of an interface function with two distin ct values identifying the two fluids. The starting point for the spati al discretization of these equations are the stabilized finite element formulations which possess good stability and accuracy properties. To increase the accuracy in modeling the interfaces, we use finite eleme nt functions corresponding to enhanced discretization at and near the interface. These functions are designed to have multiple components, w ith each component coming from a different level of mesh refinement ov er the same computational domain. The primary component of the functio ns for Velocity and pressure comes from the base mesh called Mesh-1. A subset of the elements in Mesh-1 are identified to be at or near the interface, and depending on where the interface is, this subset could change from one time level to another. A Mesh-2 is constructed by patc hing together the second-level meshes generated over this subset of el ements, and the second component of the functions for velocity and pre ssure comes from Mesh-2. For the interface function, we have a third c omponent coming from a Mesh-3 which is constructed by patching togethe r the third-level meshes generated over a subset of elements in Mesh-2 . With parallel computation of the test problems presented here, we de monstrate that the EDICT can be used very effectively to increase the accuracy of the base finite element formulations. (C) 1998 Elsevier Sc ience S.A.