Tetrahedral mesh improvement using moving mesh smoothing, lazy searching flips, and RBF surface reconstruction

Given a tetrahedral mesh and objective functionals measuring the mesh quality which take into account the shape, size, and orientation of the mesh elements, our aim is to improve the mesh quality as much as possible. In this paper, we combine the moving mesh smoothing, based on the integration of an ordinary differential equation coming from a given functional, with the lazy flip technique, a reversible edge removal algorithm to modify the mesh connectivity. Moreover, we utilize radial basis function (RBF) surface reconstruction to improve tetrahedral meshes with curved boundary surfaces. Numerical tests show that the combination of these techniques into a mesh improvement framework achieves results which are comparable and even better than the previously reported ones.Comment: Revised and improved versio

Parallel Anisotropic Unstructured Grid Adaptation

Computational Fluid Dynamics (CFD) has become critical to the design and analysis of aerospace vehicles. Parallel grid adaptation that resolves multiple scales with anisotropy is identified as one of the challenges in the CFD Vision 2030 Study to increase the capacity and capability of CFD simulation. The Study also cautions that computer architectures are undergoing a radical change and dramatic increases in algorithm concurrency will be required to exploit full performance. This paper reviews four different methods to parallel anisotropic grid generation. They cover both ends of the spectrum: (i) using existing state-of-the-art software optimized for a single core and modifying it for parallel platforms and (ii) designing and implementing scalable software with incomplete, but rapidly maturating functionality. A brief overview for each grid adaptation system is presented in the context of a telescopic approach for multilevel concurrency. These methods employ different approaches to enable parallel execution, which provides a unique opportunity to illustrate the relative behavior of each approach. Qualitative and quantitative metric evaluations are used to draw lessons for future developments in this critical area for parallel CFD simulation

VoroCrust: Voronoi Meshing Without Clipping

Polyhedral meshes are increasingly becoming an attractive option with particular advantages over traditional meshes for certain applications. What has been missing is a robust polyhedral meshing algorithm that can handle broad classes of domains exhibiting arbitrarily curved boundaries and sharp features. In addition, the power of primal-dual mesh pairs, exemplified by Voronoi-Delaunay meshes, has been recognized as an important ingredient in numerous formulations. The VoroCrust algorithm is the first provably-correct algorithm for conforming polyhedral Voronoi meshing for non-convex and non-manifold domains with guarantees on the quality of both surface and volume elements. A robust refinement process estimates a suitable sizing field that enables the careful placement of Voronoi seeds across the surface circumventing the need for clipping and avoiding its many drawbacks. The algorithm has the flexibility of filling the interior by either structured or random samples, while preserving all sharp features in the output mesh. We demonstrate the capabilities of the algorithm on a variety of models and compare against state-of-the-art polyhedral meshing methods based on clipped Voronoi cells establishing the clear advantage of VoroCrust output.Comment: 18 pages (including appendix), 18 figures. Version without compressed images available on https://www.dropbox.com/s/qc6sot1gaujundy/VoroCrust.pdf. Supplemental materials available on https://www.dropbox.com/s/6p72h1e2ivw6kj3/VoroCrust_supplemental_materials.pd

Automatic Curvilinear Quality Mesh Generation Driven by Smooth Boundary and Guaranteed Fidelity

The development of robust high-order finite element methods requires the construction of valid high-order meshes for complex geometries without user intervention. This paper presents a novel approach for automatically generating a high-order mesh with two main features: first, the boundary of the mesh is globally smooth; second, the mesh boundary satisfies a required fidelity tolerance. Invalid elements are eliminated. Example meshes demonstrate the features of the algorithm

Automatic higher order mesh generation and movement utilizing spring-field and vector-adding

In this research, an automatic, complex geometry applicable, unstructured curved 2D mesh generation method is developed. Based on this 2D method, an extension to 3D geometries is developed. The methodology of this mesh generation is to provide near-body and off-body meshes by an advancing-layer method to avoid mesh quality problems in transition areas, while using spring models to complement the advancing-layers by smoothing the mesh, especially in medial axis regions. After generating the linear mesh, a higher-order finite-element ready, curved mesh is obtained by deforming the linear mesh through “pipes” using a simple Vector-Adding approach. Different from most curved viscous mesh generation approaches, this method eschews a linear or nonlinear elasticity analogy while still providing positive-Jacobian mesh elements. In addition, the transformation from linear to curved meshes can be achieved by only deforming the necessary edges of the elements near domain boundaries while retaining the remaining non-curved edges to the benefit of numerical solvers. The CFD results of 30P30N airfoil on the curved mesh are given and are in good agreement with the experimental data. Further, a new method for moving boundary problems with viscous mesh layers is also presented. This method is an extension of the mesh generation approach above. It can be used not only for high-order mesh moving but also for high-order mesh generation. Also, based on the curved mesh deformation strategy, the method can handle high-order mesh movement or regeneration with minimal extra computational time compared with linear mesh movement. Several 2D boundary motion cases are tested including boundary translations, boundary rotations, and boundary morphing. The CFD results on the curved mesh after rotation are given and are in good agreement with the experimental data. This technique is also tested through the optimization of an airfoil to achieve a maximized lift and drag ratio. The results demonstrate that this approach can handle large boundary movements while preserving a good mesh quality

Extreme-Scale Parallel Mesh Generation: Telescopic Approach

In this poster we focus and present our preliminary results pertinent to the integration of multiple parallel Delaunay mesh generation methods into a coherent hierarchical framework. The goal of this project is to study our telescopic approach and to develop Delaunay-based methods to explore concurrency at all hardware layers using abstractions at (a) medium-grain level for many cores within a single chip and (b) coarse-grain level, i.e., sub-domain level using proper error metric- and application-specific continuous decomposition methods

Automatic generation of 3D unstructured high-order curvilinear meshes

This is the final version of the article. Available from the publisher via the DOI in this record.The generation of suitable, good quality high-order meshes is a significant obstacle in the academic and industrial uptake of high-order CFD methods. These methods have a number of favourable characteristics such as low dispersion and dissipation and higher levels of numerical accuracy than their low-order counterparts, however the methods are highly susceptible to inaccuracies caused by low quality meshes. These meshes require significant curvature to accuratly describe the geometric surfaces, which presents a number of difficult challenges in their generation. As yet, research into the field has produced a number of interesting technologies that go some way towards achieving this goal, but are yet to provide a complete system that can systematically produce curved high-order meshes for arbitrary geometries for CFD analysis. This paper presents our efforts in that direction and introduces an open-source high-order mesh generator, NekMesh, which has been created to bring high-order meshing technologies into one coherent pipeline which aims to produce 3D high-order curvilinear meshes from CAD geometries in a robust and systematic way

Turbulent Output-Based Anisotropic Adaptation

Controlling discretization error is a remaining challenge for computational fluid dynamics simulation. Grid adaptation is applied to reduce estimated discretization error in drag or pressure integral output functions. To enable application to high O(10(exp 7)) Reynolds number turbulent flows, a hybrid approach is utilized that freezes the near-wall boundary layer grids and adapts the grid away from the no slip boundaries. The hybrid approach is not applicable to problems with under resolved initial boundary layer grids, but is a powerful technique for problems with important off-body anisotropic features. Supersonic nozzle plume, turbulent flat plate, and shock-boundary layer interaction examples are presented with comparisons to experimental measurements of pressure and velocity. Adapted grids are produced that resolve off-body features in locations that are not known a priori