Lagrangian Finite Element Analysis of Newtonian Fluid Flows

A fully Lagrangian nite element method for the analysis of Newtonian ows is developed. The approach furnishes, in e ect, a Lagrangian implementation of the compressible Navier–Stokes equations. As the ow proceeds, the mesh is maintained undistorted through continuous and adaptive remeshing of the uid mass. The principal advantage of the present approach lies in the treatment of boundary conditions at material surfaces such as free boundaries, uid= uid or uid=solid interfaces. In contrast to Eulerian approaches, boundary conditions are enforced at material surfaces ab initio and therefore require no special attention. Consistent tangents are obtained for Lagrangian implicit analysis of a Newtonian uid ow which may exhibit compressibility e ects. The accuracy of the approach is assessed by comparison of the solution for a sloshing problem with existing numerical results and its versatility demonstrated through a simulation of wave breaking. The nite element mesh is maintained undistorted throughout the computation by recourse to frequent and adaptive remeshing ? 1998 John Wiley & Sons, Ltd.