No abstract

SUMMARYThe numerical analysis of two-fluid flows involves the treatment of a discontinuity that appears at the separating interface. Classical Lagrangian schemes applied to update the front position between two immiscible incompressible fluids have been long recognized to provide a sharp representation of the interface. However, the main drawback of these approaches is the progressive distortion in the distribution of the markers used to identify the material front. To avoid this problem, an interface remeshing algorithm based on the diffuse approximation of the interface curvature is proposed in this work. In addition, the remeshed front is enforced to preserve the global volume. These new aspects are incorporated in an existing fluid dynamics formulation for the analysis of two-fluid flows problems. The resulting formulation is called in this work as the moving Lagrangian interface remeshing technique (MLIRT).

No abstract

An algorithm for tetrahedron mesh generation and optimization with respect to a shape and a size criterion is presented. A well distributed set of nodes is first generated by an octree method, and the set is then triangulated. The advancing front technique is used to mesh the whole volume. Emphasis has been placed on management of the front. The method involves priority construction of enhanced quality tetrahedra. Each face is assigned to a front corresponding to the quality of the best tetrahedron which can be constructed. Elements are destroyed in the case of non-convergence. Optimization procedures make local use of the algorithm used to mesh the complete model. Industrial examples of relatively complex volumes are given, demonstrating that a high quality and optimized mesh can be obtained by the proposed method.

No abstract

No abstract

SUMMARYClassical Lagrangian schemes applied to update the front position between two immiscible incompressible fluids have been long recognized to provide a sharp representation of the interface. However, the main drawback of these approaches is the progressive distortion in the distribution of the markers used to identify the material front. To avoid this problem, a 3D interface remeshing algorithm is proposed in this work. In addition, the remeshed front is enforced to preserve the global volume. These aspects are incorporated in an existing fluid dynamics formulation for the analysis of two-fluid flows problems. The resulting formulation, called as the 3D-moving Lagrangian interface remeshing technique, is applied in the numerical analysis of two-fluid flow problems.

SUMMARYThis work presents a general and e$cient way of computing both di!use and full derivatives of shape functions for meshless methods based on moving least-squares approximation (MLS) and interpolation. It is an extension of the recently introduced consistency approach based on Lagrange multipliers which provides a general framework for constrained MLS along with robust algorithms for the computation of shape functions and their di!use derivatives. The particularity of the proposed algorithms is that they do not involve matrix inversion or linear system solving. The previous approach is limited to di!use derivatives of the shape functions and not their full derivatives which are usually much more expensive to obtain. In the present paper we propose to e$ciently compute the full derivatives by a new algorithm based on the formal di!erentiation of the previous one. In this way, we obtain a uni"ed low-cost consistent methodology for evaluating the shape functions and both their di!use and full derivatives. In the second part of the paper we introduce explicit forms of MLS shape functions in 1D, 2D and 3D for an arbitrary number of nodes. These forms are especially useful for comparing "nite element and MLS approximations. Finally we present a general architecture of an MLS program.