The solution of two-dimensional free-surface problems using automatic meshgeneration

A new method is described for the iterative solution of two-dimensional fre e-surface problems, with arbitrary initial geometries, in which the interio r of the domain is represented by an unstructured, triangular Eulerian mesh and the free surface is represented directly by the piecewise-quadratic ed ges of the isoparametric quadratic-velocity, linear-pressure Taylor-Hood el ements. At each time step, the motion of the free surface is computed expli citly using the current velocity field and, once the new free-surface locat ion has been found, the interior nodes of the mesh are repositioned using a continuous deformation model that preserves the original connectivity. In the event that the interior of the domain must be completely remeshed, a st andard Delaunay triangulation algorithm is used, which leaves the initial b oundary discretisation unchanged. The algorithm is validated via the benchm ark viscous flow problem of the coalescence of two infinite cylinders of eq ual radius, in which the motion is due entirely to the action of capillary forces on the free surface. This problem has been selected for a variety of reasons: the initial and final (steady state) geometries differ considerab ly; in the passage from the former to the latter, large free-surface curvat ures-requiring accurate modelling-are encountered; an analytical solution i s known for the location of the free surface; there exists a large body of literature on alternative numerical simulations. A novel feature of the pre sent work is its geometric generality and robustness; it does not require a priori knowledge of either the evolving domain geometry or the solution co ntained therein. Copyright (C) 1999 John Wiley & Sons, Ltd.