Arbitrary Lagrangian Eulerian approximation with remeshing for Navier–Stokes equations

An algorithm that allows remeshing in the arbitrary Lagrangian Eulerian (ALE) framework is presented. At every time step, we could triangulate the domain using either uniform size meshes or adapted meshes. We analyze the conditions when two time-advancing algorithms based on the backward Euler scheme provide identical approximations. Numerical results are presented for Navier–Stokes equations on moving domain. For three academic tests presented in this paper, the uniform size mesh technique provides more accurate results than the classical ALE method, in particular when the domain is expanding particularly fast. Copyright © 2009 John Wiley & Sons, Ltd.

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