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Lagrangian finite element analysis of Newtonian fluid flows. (English) Zbl 0945.76047
Summary: We develop a fully Lagrangian finite element method for the analysis of Newtonian flows. The approach furnishes, in effect, a Lagrangian implementation of compressible Navier-Stokes equations. As the flow proceeds, the mesh is maintained undistorted through continuous and adaptive remeshing of the fluid mass. The principal advantage of the present approach lies in the treatment of boundary conditions at material surfaces such as free boundaries, fluid/fluid or fluid/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 fluid flow which may exhibit compressibility effects. The accuracy of the approach is assessed by comparison of the solution for a sloshing problem with existing numerical results, and its versatility is demonstrated through a simulation of wave breaking. The finite element mesh is maintained undistorted throughout the computation by recourse to frequent and adaptive remeshing.

76M10 Finite element methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
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