A time-adaptive space-time finite element method for incompressible Lagrangian flows with free surfaces: computational issues

In order to further enhance the performance of the space-time Galerkin/leas t-squares method for solving incompressible Navier-Stokes problems involvin g free surfaces, issues related to the solution strategy and time adaptivit y are addressed. Due to the a priori unknown boundary positions, a nonlinea r system of equations normally arises at each space-time slab, which is sol ved by the Newton-Raphson approach. In addition: a linear system of equatio ns for velocity and pressure that provides an alternative approach to the s olution of the problem is also derived in this paper. This lineal solution scheme can significantly reduce the computational costs in terms of compute r CPU lime and memory requirements without the sacrifice of the solution ac curacy if the time-step size is sufficiently small. Furthermore, the possib ility of adaptively adjusting time-step size is fully exploited. By choosin g the Volume loss rate as an error indicator, a simple adaptive time-steppi ng scheme is presented. Finally several numerical examples are provided to assess the performances of the proposed schemes. (C) 2000 Elsevier Science S.A. All rights reserved.