José María González-Yuste

Simultaneous untangling and smoothing of tetrahedral meshes

Abstract The quality improvement in mesh optimisation techniques that preserve its connectivity are obtained by an iterative process in which each node of the mesh is moved to a new position that minimises a certain objective function. The objective function is derived from some quality measure of the local submesh , that is, the set of tetrahedra connected to the adjustable or free node . Although these objective functions are suitable to improve the quality of a mesh in which there are non- inverted elements, they are not when the mesh is tangled. This is due to the fact that usual objective functions are not defined on all R 3 and they present several discontinuities and local minima that prevent the use of conventional optimisation procedures. Otherwise, when the mesh is tangled, there are local submeshes for which the free node is out of the feasible region , or this does not exist. In this paper we propose the substitution of objective functions having barriers by modified versions that are defined and regular on all R 3 . With these modifications, the optimisation process is also directly applicable to meshes with inverted elements, making a previous untangling procedure unnecessary. This simultaneous procedure allows to reduce the number of iterations for reaching a prescribed quality. To illustrate the effectiveness of our approach, we present several applications where it can be seen that our results clearly improve those obtained by other authors.

Genetic algorithms for an improved parameter estimation with local refinement of tetrahedral meshes in a wind model

The efficiency of a mass-consistent model for wind field adjustment depends on several parameters that arise in various stages of the process. On one hand, those involved in the construction of the initial wind field using horizontal interpolation and vertical extrapolation of the wind measures registered at meteorological stations. On the other hand, the stability parameter which allows from a strictly horizontal wind adjustment to a pure vertical one. In general, the values of all of these parameters are based on empirical laws. The main goal of this work is the estimation of these parameters using genetic algorithms, such that some of the wind velocities observed at the measurement station are regenerated as accurately as possible by the model. In addition, we study the effect of the mesh refinement on the parameter estimation in several numerical experiments.

Velocity Field Modelling for Pollutant Plume Using 3-D Adaptive Finite Element Method

Air pollution models usually start from the computation of the velocity field of a fluid. In this paper, we present a model for computing that field based on the contribution of the observed wind flow and the vertical buoyancy or momentum plume rise defined by a Gaussian plume model. This initial velocity field is adjusted to verify incompressibility and impermeability conditions by using a mass consistent model. In this environmental modelling that occur in a three-dimensional domain defined over complex terrain, a mesh generator capable of adapting itself to the topographical data and to the numerical solution is essential. Here, the unstructured tetrahedral meshes are generated by combining the use of a refinement/derefinement algorithm for two-dimensional domains and a tetrahedral mesh generator based on Delaunay triangulation. Occasionally in this process, low quality or even inverted elements may appear. A simultaneous untangling and smoothing procedure allows to optimise the resulting meshes. Once we have constructed the adapted mesh in accordance with the geometrical characteristics of our domain, we use an adaptive local refinement in the plume trajectory. Finally, this model is applied in a test problem.

Parameter Estimation in a Three-Dimensional Wind Field Model Using Genetic Algorithms

The efficiency of a mass consistent model for wind field adjustment depends on several parameters that arise in various stages of the process. First, those involved in the construction of the initial wind field using horizontal interpolation and vertical extrapolation of the wind measures registered at meteorological stations. On the other hand, the Gauss precision moduli which allow from a strictly horizontal wind adjustment to a pure vertical one. In general, the values of all of these parameters are based on empirical laws. The main goal of this work is the estimation of these parameters using genetic algorithms, such that the wind velocities observed at the measurement station are regenerated as much as possible by the model.

Applications of Genetic Algorithms in Realistic Wind Field Simulations

Mass consistent models have been widely use in 3-D wind modelling by finite element method. We have used a method for constructing tetrahedral meshes which are simultaneously adapted to the terrain orography and the roughness length by using a refinement/derefinement process in a 2-D mesh corresponding to the terrain surface, following the technique proposed in [14, 15, 18]. In this 2-D mesh we include a local refinement around several points which are previously defined by the user. Besides, we develop a technique for adapting the mesh to any contour that has an important role in the simulation, like shorelines or roughness length contours [3, 4], and we refine the mesh locally for improving the numerical solution with the procedure proposed in [6]. This wind model introduces new aspects on that proposed in [16, 20, 19]. The characterization of the atmospheric stability is carried out by means of the experimental measures of the intensities of turbulence. On the other hand, since several measures are often available at a same vertical line, we have constructed a least square optimization of such measures for developing a vertical profile of wind velocities from an optimum friction velocity. Besides, the main parameters governing the model are estimated using genetic algorithms with a parallel implementation [20, 12, 26]. In order to test the model, some numerical experiments are presented, comparing the results with realistic measures.

Improved objective functions for tetrahedral mesh optimisation

The quality improvement in mesh optimisation techniques that preserve its connectivity are obtained by an iterative process in which each node of the mesh is moved to a new position that minimises a certain objective function. In general, objective functions are derived from some quality measure of the local submesh, that is, the set of tetrahedra connected to the adjustable or free node. Although these objective functions are suitable to improve the quality of a mesh in which there are non inverted elements, they are not when the mesh is tangled. This is due to the fact that usual objective functions are not defined on all R3 and they present several discontinuities and local minima that prevent the use of conventional optimisation procedures. Otherwise, when the mesh is tangled, there are local submeshes for which the free node is out of the feasible region, or this does not exist. In this paper we propose the substitution of objective functions having barriers by modified versions that are defined and regular on all R3. With these modifications, the optimisation process is also directly applicable to meshes with inverted elements, making a previous untangling procedure unnecessary.