Abstract
This paper presents an Arbitrary Lagrangian Eulerian (ALE) formulation derived from the Reynolds transport theorem to accurately solve certain problems of three-dimensional unsteady Newtonian flows with free surfaces. The analysis problems addressed are those without breaking waves or waves spilling over obstructions. The proposed method conserves mass very accurately and obtains stable and accurate results with large time steps, and even when using rather coarse meshes. The continuum mechanics equations are formulated and the three-dimensional Navier–Stokes equations are solved using a ‘flow condition based interpolation’ (FCBI) scheme for a tetrahedral finite element using finite volume concepts. Various example solutions are given to indicate the effectiveness of the solution schemes.
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