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Abstract: In a numerical simulation using the finite element method, the mesh has to be fine enough to guarantee the accuracy of the solution. However, a uniformly fine mesh will usually imply a more expensive computation. Mesh adaptation offers an effective compromise, combining a fine mesh with a low computational cost. The h-refinement consists in sub-dividing some meshes, where necessary due to numerical analysis. Some difficulties occur at the interface between two zones with different levels of refinement, if a conformal mesh is required. To maintain the compatibility, the refinement is performed by specific operations. These operations are simple, using triangles or tetrahedra, but are much more complex with a hexahedral mesh. This paper deals with conformal mesh refinement with hexahedra. A new method, which implies the use of tetrahedra and pyramids to connect the zones of different levels of refinement, is proposed. The details of the algorithm used to generate those meshes are presented. This new technique allows h-refinement to be used in numerical simulations based on hexahedra with a conformal finite element method. Finally, some numerical applications show the relevance of this technique in mechanical computation. [Copyright &y& Elsevier]

Abstract: We revisit in this paper the theory of axisymmetric vortex rings in an ideal fluid. The boundary separating the vortex ring from the external (potential) flow is assumed of elliptic shape. For a given distribution of vorticity in the vortex core, we theoretically put into evidence the critical parameter for the existence of non-trivial solutions, thus confirming the numerical observation of Durst et al. [ZAMP 32 (1981) 156]. A sharp estimation of the critical threshold is analytically derived. Theoretical predictions are confirmed by numerical simulations using finite elements. A new numerical algorithm is presented and shown to display better performances compared to previous published algorithms using finite differences. The convergence of the iterative algorithm is proved using the theory of elliptic partial differential equations with discontinuous nonlinearities. [Copyright &y& Elsevier]

Abstract: The high advanced techniques in parallel computing can be employed for a better understanding of groundwater flow fluids. Generally, the geological media are very heterogeneous and contain complex structures. Decomposing these structures into, approximately, equivalent sub-structures for a load-balancing is a major challenge. This paper proposes and analyses a new algorithm to simulate parallel flow fluid in such complex media. Fully parallel software is developed, and two well-known sparse linear solvers, based respectively on a multifrontal Cholesky factorization and an iterative structured multigrid method, are compared. The mixed finite element (MFE) method is used to discretize Darcy’s equation. Numerical examples are presented to show the efficiency and robustness of the algorithm proposed. [Copyright &y& Elsevier]

This paper presents a parallel algorithm to improve the quality of surface meshes representing models obtained from surface reconstruction, as well as models generated by the application of the Boolean and assembly operations to predefined primitives, such as spheres and blocks. The smooth surface approximation is generated in parallel, the faces are distributed evenly among the processors. Then, the surface mesh is divided into sections, which are refined first, and intersections for remeshing at the end. [ABSTRACT FROM PUBLISHER]