William Wagner Matos Lira

A modeling methodology for finite element mesh generation of multi-region models with parametric surfaces☆

Abstract This paper presents a description of the reorganization of a geometric modeler, MG, designed to support new capabilities of a topological module (CGC) that allows the detection of closed-off solid regions described by surface patches in non-manifold geometric models defined by NURBS. These patches are interactively created by the user by means of the modelers graphics interface, and may result from parametric–surface intersection in which existing surface meshes are used as a support for a discrete definition of intersection curves. The geometry of realistic engineering objects is intrinsically complex, usually composed by several materials and regions. Therefore, automatic and adaptive meshing algorithms have become quite useful to increase the reliability of the procedures of a FEM numerical analysis. The present approach is concerned with two aspects of 3D FEM simulation: geometric modeling, with automatic multi-region detection, and support to automatic finite-element mesh generation.

Boolean operations on multi-region solids for mesh generation

An algorithm for Boolean operations on non-manifold models is proposed to allow the treatment of solids with multiple regions (internal interfaces) and degenerate portions (shells and wires), in the context of mesh generation. In a solid modeler, one of the most powerful tools to create three-dimensional objects with any level of geometric complexity is the Boolean set operators. They are intuitive and popular ways to combine solids, based on the operations applied to point sets. To assure that the resulting objects have the same dimension as the original objects, without loose or dangling parts, a regularization process is usually applied after a Boolean operation. In practice, the regularization is performed classifying the topological elements and removing internal or lower-dimensional structures. However, in many engineering applications, the adopted geometric model may contain idealized internal parts, as in the case of multi-region models, or lower-dimensional parts, as in the case of solids that contain dangling slabs that are represented as zero-thickness surfaces or wireframes in the model. Therefore, the aim of this work is the development of a generic algorithm that allows the application of the Boolean set operations in a geometric modeling environment applied to finite and boundary element mesh generation. This environment adopts a non-manifold boundary representation that considers an undefined number of topological entities (group concept), and works with objects of different dimensions and with objects not necessarily plane or polyhedral (parametric curved surfaces). Numerical examples are presented to illustrate the proposed methodology.

A Three-Dimensional Adaptive Mesh Generation Approach Using Geometric Modeling With Multi-Regions and Parametric Surfaces

This work presents a methodology for adaptive generation of 3D finite element meshes using geometric modeling with multiregions and parametric surfaces, considering a geometric model described by curves, surfaces, and volumes. This methodology is applied in the simulation of stress analysis of solid structures using a displacement-based finite element method and may be extended to other types of 3D finite element simulation. The adaptive strategy is based on an independent and hierarchical refinement of curves, surfaces, and volumes. From an initial model, new sizes of elements obtained from a discretization error analysis and from geometric restrictions are stored in a global background structure, a recursive spatial composition represented by an octree. Based on this background structure, the model’s curves are initially refined using a binary partition algorithm. Curve discretization is then used as input for the refinement of adjacent surfaces. Surface discretization also employs the background octree-based refinement, which is coupled to an advancing front technique in the surface’s parametric space to generate an unstructured triangulated mesh. Surface meshes are finally used as input for the refinement of adjacent volumetric domains, which also uses an advancing front technique but in 3D space. In all stages of the adaptive strategy, the refinement of curves, surface meshes, and solid meshes is based on estimated discretization errors associated with the mesh of the previous step in the adaptive process. In addition, curve and surface refinement takes curvature information into account. Numerical examples of simulation of engineering problems are presented in order to validate the methodology proposed in this work. [DOI: 10.1115/1.4024106]

Finite element mesh generation for subsurface simulation models

This paper introduces a methodology for creating geometrically consistent subsurface simulation models, and subsequently tetrahedral finite element (FE) meshes, from geometric entities generated in gOcad software. Subsurface simulation models have an intrinsic heterogeneous characteristic due to the different geomechanics properties of each geological layer. This type of modeling should represent geometry of natural objects, such as geological horizons and faults, which have faceted representations. In addition, in subsurface simulation modeling, lower-dimension degenerated parts, such as dangling surfaces, should be represented. These requirements pose complex modeling problems, which, in general, are not treated by a generic geometric modeler. Therefore, this paper describes four important modeling capabilities that are implemented in a subsurface simulation modeler: surface re-triangulation, surface intersection, automatic volume recognition, and tetrahedral mesh generation. Surface re-triangulation is used for regenerating the underlying geometric support of surfaces imported from gOcad and of surface patches resulting from intersection. The same re-triangulation algorithm is used for generating FE surface meshes. The proposed modeling methodology combines, with some adaptation, meshing algorithms previously published by the authors. Two novel techniques are presented, the first for surface intersection and the second for automatic volume recognition. The main contribution of the present work is the integration of such techniques through a methodology for the solution of mesh generation problems in subsurface simulation modeling. An example illustrates the capabilities of the proposed methodology. Shape quality of generated triangular surface and tetrahedral meshes, as well as the efficiency of the 3D mesh generator, is demonstrated by means of this example.

Stochastic particle packing with specified granulometry and porosity

This work presents a technique for particle size generation and placement in arbitrary closed domains. Its main application is the simulation of granular media described by disks. Particle size generation is based on the statistical analysis of granulometric curves which are used as empirical cumulative distribution functions to sample from mixtures of uniform distributions. The desired porosity is attained by selecting a certain number of particles, and their placement is performed by a stochastic point process. We present an application analyzing different types of sand and clay, where we model the grain size with the gamma, lognormal, Weibull and hyperbolic distributions. The parameters from the resulting best fit are used to generate samples from the theoretical distribution, which are used for filling a finite-size area with non-overlapping disks deployed by a Simple Sequential Inhibition stochastic point process. Such filled areas are relevant as plausible inputs for assessing Discrete Element Method and similar techniques.

An OOP approach for mesh generation of multi-region models with NURBS

This paper presents an object-oriented approach for creating multi-region non-manifold models with NURBS. The main motivation is that the geometry and shape of realistic engineering objects are intrinsically complex, usually composed by several materials and regions. Therefore, automatic and/or adaptive meshing algorithms have become revealed themselves quite useful to increase the reliability of the procedures of a FEM numerical analysis. The present approach is concerned with two aspects of 3D FEM simulation: geometric modeling, with automatic multi-region detection, and support to automatic finite element mesh generation. The final objective is to use geometric models directly in numerical applications.

A hybrid parallel DEM approach with workload balancing based on HSFC

Purpose The purpose of this paper is to present a methodology of hybrid parallelization applied to the discrete element method that combines message-passing interface and OpenMP to improve computational performance. The scheme is based on mapping procedures based on Hilbert space-filling curves (HSFC). Design/methodology/approach The methodology uses domain decomposition strategies to distribute the computation of large-scale models in a cluster. It also partitions the workload of each subdomain among threads. This additional procedure aims to reach higher computational performance by adjusting the usage of message-passing artefacts and threads. The main objective is to reduce the communication among processes. The work division by threads employs HSFC in order to improve data locality and to avoid related overheads. Numerical simulations presented in this work permit to evaluate the proposed method in terms of parallel performance for models that contain up to 3.2 million particles. Findings Distinct partitioning algorithms were used in order to evaluate the local decomposition scheme, including the recursive coordinate bisection method and a topological scheme based on METIS. The results show that the hybrid implementations reach better computational performance than those based on message passing only, including a good control of load balancing among threads. Case studies present good scalability and parallel efficiencies. Originality/value The proposed approach defines a configurable execution environment for numerical models and introduces a combined scheme that improves data locality and iterative workload balancing.

A parallel DEM approach with memory access optimization using HSFC

Purpose The purpose of this paper is to present a methodology for parallel simulation that employs the discrete element method (DEM) and improves the cache performance using Hilbert space filling curves (HSFC). Design/methodology/approach The methodology is well suited for large-scale engineering simulations and considers modelling restrictions due to memory limitations related to the problem size. An algorithm based on mapping indexes, which does not use excessive additional memory, is adopted to enable the contact search procedure for highly scattered domains. The parallel solution strategy uses the recursive coordinate bisection method in the dynamical load balancing procedure. The proposed memory access control aims to improve the data locality of a dynamic set of particles. The numerical simulations presented here contain up to 7.8 millions of particles, considering a visco-elastic model of contact and a rolling friction assumption. Findings A real landslide is adopted as reference to evaluate the numerical approach. Three-dimensional simulations are compared in terms of the deposition pattern of the Shum Wan Road landslide. The results show that the methodology permits the simulation of models with a good control of load balancing and memory access. The improvement in cache performance significantly reduces the processing time for large-scale models. Originality/value The proposed approach allows the application of DEM in several practical engineering problems of large scale. It also introduces the use of HSFC in the optimization of memory access for DEM simulations.

Thermomechanical effect of vertical well drilling in salt rocks in selected cases

Purpose – The purpose of this paper is to present an analysis of the effect of the temperature on the creep deformation during vertical well drilling in salt rocks in selected cases. Design/methodology/approach – The authors performed numerical simulations by Finite Element Method, using non-linear viscoelastic models and weak thermomechanical coupling. The authors evaluated, in selected cases, the effect of temperature during salt rock vertical well drilling. Numerical examples were performed to validate the studies. More specifically, the authors considered the problem of vertical well drilling for oil exploration below these salt layers. Findings – The authors concluded that the biggest reduction in the wellbore closure rate occurs when the wellbore is at low temperature with respect to the rock initial. This is due to two factors, namely, a reduced salt viscous strain rate and the thermal strain contrary to the well radial closure caused by the temperature variation. Beyond the creep effect, the therm...