Construction of polynomial spline spaces over quadtree and octree T-meshes for its application in isogeometric analysis

[EN]We present a new strategy for construction spline spaces over hierarchical T-meshes with quad- and octree subdivision scheme.MINECO y FEDER; CONACYT-SENER Project, Fondo Sectorial, contract: 16372

Wind field simulation with isogeometric analysis

[EN]For wind field simulation with isogeometric analysis, firstly it is necessary to generate a spline parameterization of the computational domain, which is an air layer above the terrain surface. This parameterization is created with the meccano method from a digital terrain model. The main steps of the meccano method for tetrahedral mesh generation were introduced in [1, 2]. Based on the volume parameterization obtained by the method, we can generate a mapping from the parametric T-mesh to the physical space [3, 4]. Then, this volumetric parameterization is used to generate a cubic spline representation of the physical domain for the application of isogeometric analysis. We consider a mass-consistent model [5] to compute the wind field simulation in the three-dimensional domain from wind measurements or a wind forecasted by a meteorological model (for example, WRF or HARMONIE). From these data, an interpolated wind field is constructed. The mass-consistent model obtains a new wind field approaching the interpolated one, but verifying the continuity equation (mass conservation) for constant density and the impermeabilitycondition on the terrain. This adjusting problem is solved by introducing a Lagrange multiplier, that is the solution of a Poisson problem. The resulting field is obtained from the interpolated one and the gradient of the Lagrange multiplier. It is well known that if we use classical Lagrange finite elements, the gradient of the numerical solution is discontinuous over the element boundary. The advantage of using isogeometric analysis with cubic polynomial basis functions [6, 7] is that we obtain a C2 continuity for the Lagrange multiplier in the whole domain. In consequence, the resulting wind field is better approximated. Applications of the proposed technique are presented.Ministerio de Economía y Competitividad del Gobierno de España; Fondos FEDER; CONACYT-SENE

Analysis of several objective functions for optimization of hexahedral meshes

Ministerio de Educación, Cultura y Deporte MINECO; FEDE

Strategies for optimization of hexahedral meshes and their comparative study

In this work, we study several strategies based on different objective functions for optimization of hexahedral meshes. We consider two approaches to construct objective functions. The first one is based on the decomposition of a hexahedron into tetrahedra. The second one is derived from the Jacobian matrix of the trilinear mapping between the reference and physical hexahedral element. A detailed description of all proposed strategies is given in the present work. Some computational experiments have been developed to test and compare the untangling capabilities of the considered objective functions. In the experiments, a sample of highly distorted hexahedral elements is optimized with the proposed objective functions, and the rate of success of each function is obtained. The results of these experiments are presented and analyzed.Secretaría de Estado de Universidades e Investigación del Ministerio de Economía y Competitividad del Gobierno de España; Programa de FPU del Ministerio de Educación, Cultura y Deporte; Programa de FPI propio de la ULPGC; Fondos FEDE

Spline parameterization method for 2D and 3D geometries based on T-mesh optimization

[EN]We present a method to obtain high quality spline parameterization of 2D and 3D geometries for their use in isogeometric analysis. As input data, the proposed method demands a boundary representation of the domain, and it constructs automatically a spline transformation between the physical and parametric domains. Parameterization of the interior of the object is obtained by deforming isomorphically an adapted parametric T-mesh onto the physical domain by applying a T-mesh untangling and smoothing procedure, which is the key of the method. Mesh optimization is based on the mean ratio shape quality measure. The spline representation of the geometry is calculated by imposing interpolation conditions using the data provided by one-to-one correspondence between the meshes of the parametric and physical domains. We give a detailed description of the proposed technique and show some examples. Also, we present some examples of the application of isogeometric analysis in geometries parameterized with our method.Secretaría de Estado de Universidades e Investigación del Ministerio de Economía y Competitividad del Gobierno de España y fondos FEDER; Programa de FPU 12/00202 del Ministerio de Educación, Cultura y Deporte; Programa de FPI propio de la Universidad de Las Palmas de Gran Canari

The Meccano Method for Mesh Generation and Solid Parameterization

[EN]In this conference, we present the main advances in the meccano method, which was introduced by the authors in 2006 for tetrahedral mesh generation

Generación de Mallas y Simulación Numérica en Medioambiente

[ES]En esta conferencia se introducen ideas básicas sobre la simulación numérica, mediante el método de los elementos finitos (MEF), de problemas medioambientales que han sido abordados por nuestro grupo en diversos proyectos de investigación sobre simulación de campos de viento, radiación solar, contaminación atmosférica y la modelización de yacimientos de petróleo