SIAM IMR23: Program

A method for adaptive anisotropic refinement and coarsening of prismatic polyhedra

Sandeep Menon, Ansys Inc
Thomas Gessner, Ansys Inc

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Keywords: mesh adaptation, refinement, coarsening, anisotropy, polyhedra

Abstract

A method is proposed to enable the anisotropic refinement and coarsening of prismatic boundary-layer polyhedra within the context of unstructured polyhedral meshes for viscous flow simulations using computational fluid dynamics. The method is compatible with the Polyhedral Unstructured Mesh Adaption (PUMA) algorithm for the isotropic refinement and subsequent coarsening of general polyhedral cells. This allows simulations to leverage the full flexibility of polyhedral meshes for adaptive mesh refinement, while retaining the benefits of an improved accuracy-to-computational cost ratio.

Towards industrial use of anisotropic hexahedral mesh adaptation for hydrodynamic flows

Jeroen Wackers, Ecole Centrale de Nantes / CNRS
Ganbo Deng, Ecole Centrale de Nantes / CNRS
Emmanuel Guilmineau, Ecole Centrale de Nantes / CNRS
Alban Leroyer, Ecole Centrale de Nantes / CNRS
Patrick Queutey, Ecole Centrale de Nantes / CNRS

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Keywords: mesh adaptation, anisotropy, hexahedral, mesh deformation, automatic setup, ship hydrodynamics

Abstract

This paper discusses the preparation of the flow solver ISIS-CFD for industrial simulation of free-surface hydrodynamic flows with adaptive mesh refinement. To accurately capture the free surface and boundary layers, anisotropic hexahedral mesh refinement and derefinement is performed by local cell division. The adaptation is based on metric criteria which combine Hessians of the flow variables and free-surface detection. Analytical mesh deformation is used to account for body movement, while a dedicated local deformation algorithm handles the projection of the adapted mesh onto the geometry. It is shown that computational setup protocols can be defined to choose the simulation parameters, without user intervention, for large classes of simulations. Tests on different ships and lifting hydrofoils show the efficiency and versatility of the method.

Combinatorial Methods in Grid based Meshing

Henrik Stromberg, TU Clausthal
Valentin Mayer-Eichberger, University of Potsdam
Armin Lohrengel, TU Clausthal

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Keywords: mesh generation, Answer-Set-Programming, computational geometry, hex-dominant

Abstract

This paper describes a novel method of generating hex-dominant meshes using optimal subdivisions of a cube in a grid-based approach. Our method is mainly intended to be used for geometries common in mechanical engineering which need to comply with the restrictions of subtractive manufacturability. We describe how small meshes can be modeled as graphs and optimized with an Answer Set Programming. With this approach we can obtain small optimal meshes of up to 35 nodes which we call super-elements. For meshing whole parts, we first generate a coarse precursor mesh representing the bar stock. The result mesh is generated in a substantive manner by inserting and fitting the pre-generated super-elements into the precursor mesh. The resulting mesh is similar to the target geometry. Finally, the nodes are mapped to geometric entities of the target geometry to get an exact match. We demonstrate our method with multiple examples showing the strength of this approach.

Estimating the number of similarity classes for marked bisection in general dimensions

Guillem Belda-Ferrín, Barcelona Supercomputing Center
Eloi Ruiz-Gironés, Barcelona Supercomputing Center
Xevi Roca, Barcelona Supercomputing Center

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Keywords: adaption, local bisection, $n$-dimensional bisection, similarity classes

Abstract

To measure the stability of a marked bisection method, we estimate in general dimensions an upper bound of the number of generated similarity classes. Moreover, to understand the cyclic similarity structure, we estimate the number of uniform refinements required to generate all the similarity classes. We first prove that switching to the newest vertex bisection after $n$ uniform refinements is equivalent to switching after $n-2$ uniform refinements. Then, we obtain the similarity bound, a bound that we use to derive the number of uniform refinements required to generate all the similarity classes. Although the similarity bound is not tight, the results show that it estimates the magnitude of the expected number of classes. We also show the ratio of the number of similarity classes for marked bisection and newest vertex bisection. Because this ratio grows exponentially with the dimension, we conclude that marked bisection is suitable for low-dimensional applications.

Region selective subdivision of intrinsic meshes

Vijai Kumar Suriyababu, Technical University of Delft
Cornelis Vuik, Technical University of Delft
Matthias Möller, Technical University of Delft

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Keywords: intrinsic triangulations, constrained subdivision

Abstract

Intrinsic triangulations have gained significant attention in the past couple of years due to their ability to represent surface meshes in terms of edge lengths rather than vertex positions. This property allows intrinsic mesh data structures to maintain the relationship between the intrinsic mesh and its underlying extrinsic mesh, ensuring that solution fields are transferred between the two as efficiently as possible. While the use of intrinsic triangulations has been shown to offer numerous benefits, the common subdivision process has often resulted in a loss of quality. In this paper, we propose a modified version of the common subdivision that performs selective edge-edge intersections, leading to a more useful mesh in two and three dimensions when compared to the simple common subdivision previously proposed in the literature. Through this constrained subdivision method, we demonstrate the potential to retain the quality gains from intrinsic triangulations in an extrinsic setting along with some useful applications.

Surface remeshing based on conformal uniformization

Hang Si, Cadence Design Systems
Na Lei, Dalian University of Technology
Xianfeng Gu, SUNY at Stony Brook

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Keywords: surface mesh generation; conformal mapping; uniformization; Ricci flow; Delaunay refinement; adaptive sampling

Abstract

Surface meshing plays a fundamental role in CAD and CAE. This work introduces a rigorous and efficient algorithm for generating high quality triangulations on surfaces with complicated topologies based on conformal geometry. The key idea is to flatten the input surface onto a planar domain by an angle-preserving (conformal) map, then a high quality planar mesh is generated and pulled back to the 3D surface. Since the mapping is angle-preserving, the Delaunay property is preserved to the surface triangulation. Furthermore, the planar sampling density is adaptive to the surface area element and the curvature, this guarantee the surface meshing quality. By converting the 3D meshing problem to the 2D problem, this method reduces the algorithmic difficulty and improves the computational efficiency and mesh quality. Our experimental results demonstrate the efficiency and efficacy of the proposed algorithm.

Surface cross field generation based on characteristic class of fiber bundle

Zhongxuan Luo, Dalian University of Technology
Yiming Zhu, Dalian University of Technology
Xiaopeng Zheng, Dalian University of Technology
Na Lei, Dalian University of Technology
Hang Si, Cadence Design System
Xianfeng Gu, SUNY at Stony Brook

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Keywords: surface cross field generation, fiber bundle, characteristic class, topological obstruction, holonomy, harmonic forms, Ricci flow

Abstract

Constructing smooth cross fields on surfaces plays a crucial role for structured quad-mesh generation. This work develop a theoretical framework, which treats a cross field as a section of the cross bundle over the surface, the singularities as the topological obstruction to the existence of global section, namely the characteristic class of the bundle. The work proves the necessary and sufficient condition for the singularity configuration of cross fields based on Ricci flow, which leads to a rigorous and efficient algorithm for cross field construction. Experimental results demonstrate the efficiency and efficacy of the algorithm.

Isogeometric boundary-conforming body-in-white crash model construction, analysis, and comparison with FEM model

Kendrick M. Shepherd, Brigham Young University
Xianfeng David Gu, The State University of New York at Stony Brook
Thomas J. R. Hughes, The University of Texas at Austin

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Keywords: mesh generation, isogeometric analysis, body-in-white, crash, quadrilateral, splines

Abstract

In this paper, we discuss model generation to rebuild the body-in-white of a 1996 Dodge Neon finite element model into a isogeometric conforming analysis-suitable crash model. We then perform the first known boundary-fit isogeometric body-in-white crash analysis of the vehicle and compare results achieved by traditional finite element methods. Results indicate the value and potential of high-order meshes in analysis.

Towards an automated mesh smoother for high-order meshes: representing the boundary by a level set function

Veselin Dobrev, Lawrence Livermore National Laboratory
Patrick Knupp, Dihedral LLC
Tzanio Kolev, Lawrence Livermore National Laboratory
Ketan Mittal, Lawrence Livermore National Laboratory
Vladimir Tomov, Lawrence Livermore National Laboratory

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Keywords: implicit geometry, level set function, distance solver

Abstract

This research note presents an algorithm that takes an input mesh and constructs a finite element function, on an automatically defined background mesh, whose zero level set agrees with the boundary of the input mesh. The input does not include any additional geometric information except the mesh itself. A critical requirement for this algorithm is to define gradients of the constructed level set function both inside and outside of the input domain. The main challenges for this construction is to produce a smooth field, on both sides of the boundary, and to obtain a zero level set that agrees with the input domain. This algorithm is a first step in developing an automated mesh smoother that takes an input mesh, without any extra geometric information, and optimizes its quality by node movement of all internal and boundary nodes.

Accelerating high-order mesh optimization: metric linearization and partial assembly

Ketan Mittal, Lawrence Livermore National Laboratory
Jorge-Luis Barrera, Lawrence Livermore National Laboratory
Jean-Sylvain Camier, Lawrence Livermore National Laboratory
Veselin Dobrev, Lawrence Livermore National Laboratory
Patrick Knupp, Dihedral LLC
Tzanio Kolev, Lawrence Livermore National Laboratory
Mathias Schmidt, Lawrence Livermore National Laboratory
Kenneth Swartz, Lawrence Livermore National Laboratory
Vladimir Tomov, Lawrence Livermore National Laboratory
Daniel Tortorelli, Lawrence Livermore National Laboratory

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Keywords: Mesh optimization, High-Order, Finite elements, GPUs, Matrix-free methods

Abstract

We present a new GPU-oriented mesh optimization method for high-order finite elements. The mesh optimization framework is based on the Target-Matrix Optimization Paradigm (TMOP) where a mesh quality metric and geometric parameters (shape, size, and/or orientation) prescribed at each point in the domain are used to define an objective function. This objective function is minimized using the Newton’s method by solving a global system over the entire computational mesh. A key property of our TMOP-based approach is that the mesh optimization process is recast in terms of finite element operations, which allows us to utilize recent advances in the field of GPU-accelerated high-order finite element algorithms. Using tensor factorization and a matrix-free approach, we demonstrate improved performance compared to traditional full finite element matrix assembly. Additionally, we introduce linearization of the nonlinear TMOP mesh quality metrics, which allows us to further reduce the computational cost associated with the assembly and solve of the global system for mesh optimization. We describe the major mathematical components of the proposed method along with their efficient GPU implementation. In addition, we propose an easily reproducible mesh optimization test that can serve as a performance benchmark for the mesh optimization community.

A penalty based genetic algorithm for mesh optimization of 2D non-convex polygons

Olivier Rodrigues Gouveia, CDRSP-IPLeiria and IdMEC-IST
José Miranda Guedes, IdMEC-IST
Rui Barreiros Ruben, CDRSP-IPLeiria

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Keywords: mesh generation, mesh optimization, genetic algorithm, non-convex polygon

Abstract

Mesh quality is a crucial aspect when dealing with partial differential equations (PDEs) as it affects both solution accuracy and respective solving time. Optimization of 2D complex domains with non-convex boundary can be difficult to perform using classical gradient-based optimization methods with boundary inequality constrains as they fail to properly define the non-convex search space of the design variables. The proposed procedure uses an evolutionary optimization method, a genetic algorithm (GA), with a penalty-based cost function to obtain the optimal coordinates for inner nodes of generic non-convex polygons meshes with triangular elements.

Optimizing high-order tet meshes for smoothed particle hydrodynamics setup with the target matrix optimization paradigm

Walter Nissen, Lawrence Livermore National Laboratory
Michael Stees, Lawrence Livermore National Laboratory
J. Michael Owen, Lawrence Livermore National Laboratory
Steven Owen, Sandia National Laboratories

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Keywords: mesh optimization, smoothed particle hydrodynamics, tet, target matrix optimization paradigm

Abstract

Smoothed Particle Hydrodynamics (SPH) is a newer simulation method that enables the flexible modeling of highly dynamic, fractured problem domains, such as a planetary defense scenario with an impactor hitting an asteroid at several kilometers per second. While a meshless method, it still has stringent requirements for spatial discretization that must be honored to produce accurate simulation results. Current setup methods tend toward the manual and are customized for each geometry. Ideally we would be able to use an automatically generated tet mesh as the starting point, and optimize it for SPH. For maximum freedom, we use a high-order mesh generated with CUBIT and leverage the Target Matrix Optimization Paradigm (TMOP). Our early results show only a small improvement but the method has a lot of potential.

Block-structured quad meshing for supersonic flow simulations

Claire Roche, CEA
Franck Ledoux, CEA
Jérôme Breil, CEA
Thierry Hocquellet, CEA

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Keywords: Quadrilateral mesh generation, blocking, supersonic flow, computational fluid dynamics

Abstract

Quad meshing is a very well-studied domain for many years. While the problem can be globally considered as solved, many approaches do not provide suitable inputs for Computational Fluid Dynamics (CFD) and in our case for supersonic flow simulations. Such simulations require a very strong control on the cell size and direction. To our knowledge, engineers ensure this control manually using interactive software. In this work we propose an automatic algorithm to generate full quadrilateral block structured mesh for the purpose of supersonic flow simulation. We handle some simulation input like the angle of attack and the boundary layer definition. Our approach generates adequate 2D meshes and is designed to be extensible in 3D.

Machine Learning Classification and Reduction of CAD Parts for Rapid Design to Simulation

Steven James Owen, Sandia National Laboratories
Armida Carbajal, Sandia National Laboratories
Matthew Peterson, Sandia National Laboratories
Corey Ernst, Sandia National Laboratories

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Keywords: machine learning, classification, CAD, geometry simplification

Abstract

We demonstrate machine learning methods to reduce bottlenecks in CAD-to-simulation workflows for critical analysis. Classification of common mechanisms such as fasteners and springs requiring common simplification and preparation procedures are first addressed. We introduce a new topology-based method for extracting features from CAD parts based on geometry queries from a third-party CAD kernel. A supervised learning classification procedure is then used to predict its categorization from a rage of pre-defined categories. We demonstrate improved performance for our classification procedures over similar published work. Also demonstrated are new reduction operations to meet analysis input specifications that rapidly transform CAD parts identified as fasteners and springs into simulation-ready proxies. We also introduce a new in-situ classification tool that allows for custom categorization and easy addition of user-defined training data.

Predicting the near-optimal mesh spacing for a simulation using machine learning

Callum Lock, Swansea University
Oubay Hassan, Swansea University
Ruben Sevilla, Swansea University
Jason Jones, Swansea University

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Keywords: Mesh generation, Spacing function, Machine learning, Near-optimal mesh prediction, Computational fluid dynamics

Abstract

This paper presents a novel approach, based on neural networks, to predict the mesh spacing for a simulation by making use of the vast amount of simulations that are currently available to industry. The main idea is to compute a spacing function suitable to capture every solution available. The spacing function is then interpolated into a background mesh. A conservative interpolation strategy is proposed to ensure that the meshes that the spacing function in the coarse mesh does not under-resolve the spacing on the available, fine mesh. This step allows homogenising of the data in such a way that a neural network can be employed to predict the spacing at the background mesh. Once the neural network is trained, it can be used to predict the spacing at the nodes of the background mesh, so that near-optimal meshes can be produced for new cases. Numerical examples are used to show the potential of the proposed approach. In addition, a detailed comparison is presented with respect to a recently proposed NN approach in which the location, strength and radius of influence of a set of point sources are predicted.

Limits and prospects of polycube labelings

Sébastien Mestrallet, CEA
François Protais, INRIA
Christophe Bourcier, CEA
Franck Ledoux, CEA

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Keywords: polycube, hexahedral meshing, mesh generation, computational geometry

Abstract

Polycubes have been a fruitful approach for all-hexahedral mesh generation, thanks to an attractive robustness/quality trade-off. Starting from a tetrahedral mesh of the input shape, a polycube can be easily represented by associating one of the six signed orthogonal direction ±{X, Y, Z} to boundary triangles, called labeling. Not all labelings induce polycubes, therefore validity criteria have been proposed. Despite satisfactory in most cases, they are neither necessary nor sufficient. By presenting failure cases, we open the discussion towards new approaches to discriminate between valid and invalid polycube labelings.

Optimally convergent isoparametric P2 mesh generation

Arthur Bawin, UCLouvain/Polytechnique Montreal
André Garon, Polytechnique Montreal
Jean-François Remacle, UCLouvain

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Keywords: mesh generation, high-order mesh, interpolation error, anisotropic mesh, metric

Abstract

This paper describes a framework for the generation of $P^2$ isoparametric meshes in two dimensions. It is an extension of existing metric-based methods for high-order straight-sided mesh adaptation to curved meshes. Starting with an interpolation error estimate for curved trajectories, we compute an optimal metric field using a generalization of the log-simplex algorithm for high-order metrics. A straight quasi-unit mesh is generated in a frontal approach, then the edges are curved to minimize their length in the chosen metric. Convergence studies are performed on simple test cases. In particular, optimal convergence rates (third order) are reached even when the edges curvature decreases at the same rate as the edge length.

Towards a volume mesh generator tailored for NEFEM

Xi Zou, Swansea University
Sui Bun Lo, Swansea University
Ruben Sevilla, Swansea University
Oubay Hassan, Swansea University
Kenneth Morgan, Swansea University

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Keywords: mesh generation, exact geometry, NURBS-enhanced FEM, de-featuring

Abstract

The conversion of digital models from computer-aided design (CAD) to meshes for computer-aided engineering (CAE) is a well-known bottleneck, because of the amount of human intervention required in the cumbersome de-featuring process. This paper introduces the strategy to address this issue by generating the geometric-persistent volume mesh tailored for the NURBS-enhanced finite element method (NEFEM). The NEFEM has been developed to decouple the geometry representation and the numerical approximation to address this issue. NEFEM uses CAD data, the non-uniform rational B-spline (NURBS) that describe the boundary representation (B-rep), to describe the geometry of the computational domain, and it adopts polynomial shape functions for the numerical approximation of the unknown solution. The need for de-featuring is avoided by NEFEM, and the geometric error is completely removed. As a dedicated NEFEM mesh generator is crucial for problems involving complex geometries, this paper introduces the strategy devised to generate volume meshes tailored for NEFEM solvers. The proposed approach is based on previously developed NEFEM surface mesh generation method, and new requirements for validity checks are imposed for the volume mesh generation. A layer of NEFEM volume elements is firstly created, followed by the interior volume mesh which can be obtained from a standard mesh generator. The resulting mesh maintains the exact geometric B-rep, and the element sizes are fully dominated by the user-defined spacing and not by the presence of small geometric features. Examples are presented for an illustrative demonstration of the proposed technique.

Curvilinear mesh generation for the high-order virtual element method (VEM)

Kaloyan Kirilov, Imperial College London
Joaquim Peiro, Imperial College London
Mashy Green, King's College London
David Moxey, King's College London
Lourenço Beirão da Veiga, University of Milano-Bicocca

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Keywords: Virtual element method; High-order mesh generation; Curvilinear polygonal meshes

Abstract

We present a proof-of-concept methodology for generating curvilinear polygonal meshes suitable for high-order discretizations by the Virtual Element Method (VEM). A VEM discretization requires the definition of a set of boundary and internal points that are used to interpolate the approximation functions and to evaluate integrals by means of suitable quadratures. The procedure to locate these points on the boundary borrows ideas from previous work on a posteriori high-order mesh generation in which the geometrical inquiries to a B-rep of the computational domain are performed via an interface to CAD libraries. Here we describe the steps of the procedure that transforms a straight-sided polygonal mesh, generated using third-party software, into a curvilinear boundary-conforming mesh. We discuss criteria for ensuring and verifying the validity of the mesh. Finally, using the Laplace equation with Dirichlet boundary conditions as a model problem, we show that VEM discretizations on such meshes achieve the expected rates of convergence as the mesh resolution is increased.

Refining simplex points for scalable estimation of the Lebesgue constant

Albert Jiménez-Ramos, Barcelona Supercomputing Center
Abel Gargallo-Peiró, Barcelona Supercomputing Center
Xevi Roca, Barcelona Supercomputing Center

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Keywords: optimization, simplices, adaptivity, point refinement, Lebesgue constant

Abstract

To estimate the Lebesgue constant, we propose a point refinement method on the $d$-dimensional simplex. The proposed method features a smooth gradation of the point resolution, neighbor queries based on neighbor-aware coordinates, and a point refinement that algebraically scales as $(d+1)d$. Remarkably, by using neighbor-aware coordinates, the point refinement method is ready to automatically stop using a Lipschitz criterion. For different polynomial degrees and point distributions, we show that our automatic method efficiently reproduces the literature estimations for the triangle and the tetrahedron. Moreover, we efficiently estimate the Lebesgue constant in higher dimensions. Accordingly, up to six dimensions, we conclude that the point refinement method is well-suited to efficiently estimate the Lebesgue constant on simplices. In perspective, for a given polynomial degree, the proposed point refinement method might be relevant to optimize a set of simplex points that guarantees a small interpolation error.

A data-driven proactive mesh refinement framework for computational fluid dynamics simulations in converging-diverging nozzles

Jaeseung Lee, Incheon National University
Hyunseok Roh, Centus
Jibum Kim, Incheon National University

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Keywords: adaptive mesh refinement, computational fluid dynamics, converging-divering nozzles

Abstract

In most computational fluid dynamics (CFD) simulations, an adaptive mesh refinement (AMR) technique, which refines the critical areas where solution accuracy is predicted to be low, is frequently used. However, for complex CFD simulations such as large-scale Navier-Stokes equations, determining a solution during the AMR process is computationally expensive and slow. Therefore, if we could preemptively and accurately predict the appropriate mesh density for the analysis target before performing CFD simulations, we expect that both the accuracy and efficiency of CFD simulations significantly improve. In this study, we assume a CFD simulation based on the Navier-Stokes equation where a shock occurs inside a jet ejected through a converging–diverging (CD) nozzle. This is considered as a difficult problem because the shock wave patterns inside the jet significantly vary according to the nozzle expansion ratio, which is the ratio between the nozzle throat and the nozzle exit inside the CD nozzle, and accordingly, the critical areas that require mesh refinement also significantly vary. We propose a data-driven proactive mesh refinement framework that learns the shock locations and corresponding optimal mesh refinement level in each element inside the jet with respect to various CD nozzle geometries and expansion ratios. Then, the proposed neural network accurately predicts the optimal mesh refinement level and finally produces high-quality refined meshes under a given CD nozzle geometry and expansion ratio condition.

t8code v. 1.0 - modular adaptive mesh refinement in the exascale era

Johannes Holke, German Aerospace Center (DLR)
Carsten Burstedde, University of Bonn
David Knapp, German Aerospace Center (DLR)
Lukas Dreyer, German Aerospace Center (DLR)
Sandro Elsweijer, German Aerospace Center (DLR)
Veli Ünlü, German Aerospace Center (DLR)
Johannes Markert, German Aerospace Center (DLR)
Ioannis Lilikakis, German Aerospace Center (DLR)
Niklas Böing, German Aerospace Center (DLR)
Prasanna Ponnusamy, German Aerospace Center (DLR)
Achim Basermann, German Aerospace Center (DLR)

Link to paper

Keywords: mesh management, adaptive mesh refinement, numerical simulation, high performance computing, exascale

Abstract

In this note we present version 1.0 of our software library t8code for scalable dynamic adaptive mesh refinement (AMR) officially released in 2022. t8code is written in C/C++, open source, and readily available at www.dlr-amr.github.io/t8code. The library provides fast and memory efficient parallel algorithms for dynamic AMR to handle tasks such as mesh adaptation, load-balancing, ghost computation, feature search and more. t8code can manage meshes with over one trillion mesh elements and scales up to one million parallel processes. It is intended to be used as mesh management back end in scientific and engineering simulation codes paving the way towards high-performance applications of the upcoming exascale era.

An initial refinement is unnecessary for a linear conforming closure of the refinement by newest vertex bisection

Lukas Gehring, Friedrich-Schiller-Universität Jena

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Keywords: newest vertex bisection, standard bisection, adaptive mesh refinement, simplicial, BDV theorem, initialization problem, virtual simplices, weak initial conditions

Abstract

An arbitrary n-dimensional simplicial complex is initialised for adaptive mesh refinement by standard bisection (aka newest vertex bisection) simply and quickly without an initial refinement splitting any original simplex into many ones. It requires an efficient algorithm that colours the nodes of the initial triangulation (any number of colours is admissible, fewer colours are better) as a missing link. The theorem of Binev, Dahmen, and DeVore about the ratio of the total number of bisected and the total number of marked simplices is extended to refinements of a triangulation initialised in that way.

Preparing non-conforming meshes of B-rep NURBS for DG-BEM simulations

Abdullah Ali, Graz University of Technology
Benjamin Marussig, Graz University of Technology

Link to paper

Keywords: computer aided geometric design, non-conforming mesh, trimmed geometries, DG-BEM

Abstract

Accommodating the flexibility of B-Rep NURBS with the strict meshing requirements of downstream applications such as numerical analysis involves numerous issues. Generating a valid volume mesh and trimming on NURBS, in particular, present severe challenges.

The discontinuous Galerkin boundary element method (DG-BEM) allows for simulations on non-conforming sur- face meshes, alleviating the need for volumetric discretization. Furthermore, the non-conforming meshes reduce requirements on trimmed NURBS. Yet, non-conforming boundaries of the mesh must provide some connectivity information for the DG-BEM simulation. The algorithm developed in this work automatically determines where to join the NURBS patches and subsequently generates the connectivity information on associated meshes.

Several test examples, including models from our industrial partner GIPRO, demonstrate the performance of our approach. In addition, subsequent electrostatic simulation results are shown.

An ergonomic approach to topological transformations of unstructured meshes

Daniel Shapero, University of Washington

Link to paper

Keywords: mesh generation, computational geometry, algebraic topology

Abstract

In this paper, we will describe an approach to performing local transformations to the topology of an unstructured mesh. Our approach, borrowing some ideas from algebraic topology, represents the mesh topology using linear operators. We can then define transformations through purely linear algebraic means. This choice of representation makes for much easier verification of the transformation kernels.

An actuator disc level set model for wind farm mesh generation and adaptation

Abel Gargallo-Peiró, Barcelona Supercomputing Center
Gonzalo Revilla, Universitat Politecnica de Catalunya
Matias Avila, Barcelona Supercomputing Center
Sonia Fernandez-Mendez, Universitat Politecnica de Catalunya
Guillaume Houzeaux, Barcelona Supercomputing Center

Link to paper

Keywords: level set, mesh adaptation, wind farms, actuator disc

Abstract

We present a level set approach to discretize the actuator disc model of the turbines of a wind farm. We represent the actuator disc geometry using a level set function that describes the actuator disc boundary. Instead of treating the disc as a geometry at the preprocessing step, we use an adaptive process to discretize the level set actuator disc representation. One of the advantages of the level set approach is that it can be coupled with standard solution driven adaptation to simultaneously adapt the mesh to both the geometry and the solution. In addition, the flexibility of the level set representation allows modifying the geometric configuration according to the actual flow, enabling the reorientation of the turbines during the simulation. We present several results to validate and illustrate the advantages of the proposed approach.