International journal of computational fluid dynamics · 1996 · 72 citations · 7 references
EngineeringComputational EngineeringMechanical EngineeringComputational Fluid DynamicsComputational MechanicsFluid DynamicsComputational AerodynamicsFinite Element FormulationFree-surface FlowNavier-stokes EquationsSurface TensionUnsteady AerodynamicsCurvatureFree Surface ModelingFree-surface Flow ModelingFree-surface HydrodynamicsGalerkin DiscretizationMesh RegularityNavier-stokes SolversUnsteady Flow
Because of its great adaptability, the Arbitrary Lagrangian Eulerian (ALE) method is often used to solve the Navier-Stokes equations with a free surface. The kinematic condition relating the normal velocity to the mesh velocity suggests a simple way to move the domain, but it leads to unstable schemes in many cases. A method to take into account the non-linearity of the free surface is presented in this paper and integrated into a Finite Method with Galerkin characteristics. A variational form of the surface tension is used to overcome the difficulty of estimating the main curvature of the surface grid. A stability estimate is then established on the global scheme, under regularity conditions on the grid.
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