Algorithm 751: TRIPACK: a constrained two-dimensional Delaunay triangulation package
ACM Transactions on Mathematical Software (TOMS)
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In this paper we present a new local remeshing algorithm that is dedicated to the problem of erosion in finite element models whose grid follows the movement of the free surface. The method, which we name Surface Lagrangian Remeshing (SLR), is adapted to 2D Lagrangian models which couple surface erosion with deformation of Earth materials. The remeshing procedure preserves nodes defining the surface submitted to erosion and removes nodes belonging to surface elements whose internal angles or area is critically low. This algorithm is ideally suited to track long term surface evolution. To validate the method we perform a set of numerical tests, using triangular finite elements, which compare the results obtained with the SLR algorithm with global remeshing and with analytical results. The results show good agreements with analytical solutions. Interpolation errors associated with remeshing are generated locally and numerical diffusion is restricted to the remeshed domain itself. In addition this method is computationally costless compared to classical global remeshing algorithm. We propose to couple the SLR method with the Dynamical Lagrangian Remeshing (DLR) algorithm to enable local remeshing only of Lagrangian models coupling large deformation of Earth materials with large erosion.