A new Lagrangian finite element method for unsteady viscous free surface fluid flow (Q1094233)

A new Lagrangian finite element formulation is presented for time- dependent incompressible free surface fluid flow problems described by the Navier-Stokes equations. The partial differential equations describing the continuum motion of the fluid were discretized using a Galerkin procedure in conjunction with the finite element approximation. The triangular finite elements are used to represent the dependent variables of the problem. An effective time integration procedure is introduced and provides the viable computational method for solving problems with equality of representation of the pressure and velocity fields. Its success has been attributed to the strict enforcement of the continuity constraint at every stage of the iterative process. The capabilities of the analysis procedure and the computer programs were demonstrated through the solution of several problems in viscous free surface fluid flow. Comparisons of results are presented with previous theoretical, numerical and experimental results.