SUMMARYA new indirect way of producing all-quad meshes is presented. The method takes advantage of a well known algorithm of the graph theory, namely the Blossom algorithm that computes the minimum cost perfect matching in a graph in polynomial time. The new Blossom-Quad algorithm is compared with standard indirect procedures. Meshes produced by the new approach are better both in terms of element shape and in terms of size field efficiency.

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A novel numerical method for solving three-dimensional two phase flow problems is presented. This method combines a quadrature free discontinuous Galerkin method for the level set equation with a pressure stabilized finite element method for the Navier Stokes equations.The main challenge in the computation of such flows is the accurate evaluation of surface tension forces. This involves the computation of the curvature of the fluid interface. In the context of the discontinuous Galerkin method, we show that the use of a curvature computed by means of a direct derivation of the level set function leads to inaccurate and oscillatory results. A more robust, second-order, least squares computation of the curvature that filters out the high frequencies and produces converged results is presented.This whole numerical technology allows to simulate a wide range of flow regimes with large density ratios, to accurately capture the shape of the deforming interface of the bubble and to maintain good mass conservation.