Global Remeshing Research Articles

A computational methodology for automatic two-dimensional anisotropic mesh generation and adaptation

This paper describes a versatile computational program for automatic two-dimensional mesh generation and remeshing adaptation of triangular, quadrilateral and mixed meshes. The system is flexible to be incorporated into an adaptive global or local remeshing procedure and for generating both, iso and anisotropic meshes. The main contribution of this work is to extend well established procedures for the generation and adaptation of both, iso and anisotropic triangular meshes, such as local and global remeshing as well as boundary layer mesh generation, to deal with iso and anisotropic quadrilateral and mixed meshes. Several examples are presented to illustrate the quality of the meshes produced, and the flexibilities of the computational system.

3D transient fixed point mesh adaptation for time-dependent problems: Application to CFD simulations

This paper deals with the adaptation of unstructured meshes in three dimensions for transient problems with an emphasis on CFD simulations. The classical mesh adaptation scheme appears inappropriate when dealing with such problems. Hence, another approach based on a new mesh adaptation algorithm and a metric intersection in time procedure, suitable for capturing and track such phenomena, is proposed. More precisely, the classical approach is generalized by inserting a new specific loop in the main adaptation loop in order to solve a transient fixed point problem for the mesh–solution couple. To perform the anisotropic metric intersection operation, we apply the simultaneous reduction of the corresponding quadratic form. Regarding the adaptation scheme, an anisotropic geometric error estimate based on a bound of the interpolation error is proposed. The resulting computational metric is then defined using the Hessian of the solution. The mesh adaptation stage (surface and volume) is based on the generation, by global remeshing, of a unit mesh with respect to the prescribed metric. A 2D model problem is used to illustrate the difficulties encountered. Then, 2D and 3D complexes and representative examples are presented to demonstrate the efficiency of this method.

Numerical modeling of crack propagation and shielding effects in a striping network

Thermal fatigue cracking is observed in some components of nuclear power plants. The residual lifetime prediction of cracked components is necessary to determine maintenance programs. An automatic procedure is developed for 2D modeling of multiple crack propagation within the finite element software Code_Aster ® to evaluate the crack growth rate and shielding effects in a multicracked structure in thermomechanical fatigue. It consists in a global remeshing method to model crack growth and includes a propagation strategy based on the crack length increment. A set of parametric studies is analyzed for a cracked pipe to evaluate the influence of geometrical and loading parameters on the residual lifetime of the crack network.

Adaptive tetrahedral meshing in free-surface flow

An unstructured, three-dimensional, moving-mesh algorithm is developed for free-surface flows with the capability of simulating large deformation. A robust edge swapping algorithm and an optimization-based mesh smoothing algorithm are used to improve mesh quality as the interface deforms. The edge swapping algorithm uses an optimal swap sequence to transform configurations with several tetrahedra sharing a common edge. The optimization-based mesh smoothing relocates vertex position so that the minimum quality of the incident cells is maximized. Also, edge contraction and bisection are used to adjust the mesh resolution according to surface curvature. These local refinements effectively maintain good mesh quality and appropriate mesh size while avoiding global re-meshing. This scheme’s robustness and accuracy are demonstrated with deforming liquid ligaments, periodic jets, and colliding droplets.

Anisotropic mesh adaptation for 3D flows on structured and unstructured grids

This paper presents a mesh optimization methodology in three dimensions, MOM3D. An initial mesh is continually adapted during the solution process without the need for global remeshing. The adaptation procedure uses an interpolation error estimate whose magnitude and direction are controlled by the Hessian, the matrix of second derivatives of the solution. This metric error is projected over mesh edges and drives the nodal movement scheme as well as the edge refinement and coarsening strategies. These operations yield highly anisotropic grids in which the mesh movement significantly contributes to the stretching and realignment of the edges along unidirectional features of flow problems. The results presented have been chosen to illustrate some important points. First, the method is gauged on problems with exact solutions, demonstrating good agreement between the error estimate and the true error as well as an equidistribution of the error. The cost-effectiveness of grid adaptation is then addressed by determining the size of an anisotropic grid that would be equivalent to that of a given non-adapted finer grid for the same error level. The capture of sharp discontinuities through highly anisotropic grids is illustrated on a transonic flow. Flow in a gas turbine combustor demonstrates how automatically generated meshes can sometimes cause convergence difficulties and how mesh adaptation can cure these ills. Finally, the flow over a wing–nacelle–pylon configuration is studied to further validate the solver–mesh adaptation capabilities by comparing the numerical results against experiments.

The algorithm of automatic local mesh subdivision and its application to finite-element analysis of a large deformation forming process

Abstract An algorithm of the automatic local mesh subdivision (ALMS) is proposed as a weak remeshing technique for the finite-element analysis of large deformation forming processes. In order to verify the effectiveness of the proposed technique, a backward extrusion process of IN718 forging was simulated by incorporating the ALMS into the viscoplastic finite-element method (FEM). The numerical results show that the ALMS is effective in eliminating the interference of the workpiece with the dies and in reducing the frequency of global remeshing. Moreover, combining the ALMS with the global remeshing technique will increase the accuracy and the efficiency of the finite-element simulation.

Improved ALE mesh velocities for moving bodies

A Laplacian smoothing of the mesh velocities with variable diffusivity based on the distance from moving bodies is introduced. This variable diffusivity enforces a more uniform mesh velocity in the region close to the moving bodies. Given that in most applications these are regions where small elements are located, the new procedure decreases element distortion considerably, reducing the need for local or global remeshing, and in some cases avoiding it altogether.

Global and local remeshing algorithms for compressible flows

A new adaptive remeshing approach for unstructured meshes, which includes the error indicator, global and local mesh regeneration techniques, has been developed in this paper. In this approach, nodes are first distributed according to the remeshing parameters, and those nodes are connected into a complete mesh. The concepts of side-based and vertex-based fronts are introduced to achieve the triangulation. According to the CPU time and the versatility, the vertex-based triangulation technique is proved to be more efficient. By using vertexbased triangulation approach, a local remeshing method, which regenerates only some regions of the flow domain, is presented. To demonstrate the reliability and availability of the proposed procedure, several compressible flow problems are investigated. The regular/stretched triangles and the mixed type of triangular and quadrilateral stretched elements are used. In this work, the Euler equations are solved by the multi-step Runge-Kutta Galerkin finite element methods. From the numerical results, the approaches, which employ the directionally stretched elements, are effective and suitable for treating the flow problems with one-dimensional features. The development of the local remeshing algorithm for unsteady flows is worthwhile and important.

Global and local remeshing algorithms for compressible flows

Global and local remeshing algorithms for compressible flows

An adaptive mesh refinement for the finite element method. 2nd report. h-method by global remeshing scheme.

A new mesh refinement approach on h-adaptation for FEM is discussed in this paper. Since there are some limitations in the r-method, especially for problems with rather complicated domains, h-refinement was supposed to be an alternative for such problems. An ordinary local remeshing approach in the h-method has a great difficulty in controlling the mesh size depending on the error measures. As a result, the number of elements is very easily increased, and the computational efficiency in FEM is decreased. The purpose of our global remeshing scheme reported in this paper is to solve these problems. Our approach can be summarized as follows: generate subdomain data based on error measure, input these data into the automatic mesh generator which supports the subdomain data structure, then get very smooth and controlled refined meshes. Its effects are evaluated with several examples on both stress concentration problem and conductive heat transfer problem.