Characteristics AtE Method for the unsteady 3 n Navier - Stokes Equations with a Free Surface

Because of its great adaptability. the Arbitrary Lagrangian Eulerian (ALE) method is ofrer" used to solve the Navier-Stokes equations v/itb;.fr; surface. rn,i ti".,i*tl" """aiii"t relating the normal velocity to the mesh yelocity suggests a simple way to move the domain,but it leads to uostable schemes in manycases. A method to takeiato account he tronJinearity of the freesurface.is presented in this paper and integ."t"a hi" "-eirii" Method with Galerkin characteristiis. A variational form ofthe ruri"6 t"nrior ir orJ to overcome the dimculty of estimating the main cuNature of the surface crid. A stabifit; estimate is the! established otr thegl;bal scheme, under regularity"o"aitlil, oo G g11al