Parallel Unstructured Quadrilateral Mesh Generation

Multi-objective unstructured triangular mesh generation for use in hydrological and land surface models

The 1st AIAA Geometry and Mesh Generation Workshop (GMGW-1) was held in conjunction with the AIAA Aviation Forum and Exposition 2017 and in collaboration with the 3rd AIAA Computational Fluid Dynamics (CFD) High Lift Prediction Workshop (HiLiftPW-3). As the first AIAA workshop on these topics, GMGW-1's broad objectives were to assess the current state-of-the art in geometry preprocessing and mesh generation technology as well as software as applied to aircraft and spacecraft systems. The workshop was intended to identify and develop understanding of areas of needed improvement in terms of performance, accuracy, and applicability. It was also to provide a foundation for documenting best practices for geometry preprocessing and mesh generation. The genesis of GMGW-1 is found in the indictments levied against geometry preprocessing and mesh generation - not undeservedly - by the NASA CFD Vision 2030 Study. In order to create a reference against which future progress in geometry preprocessing and mesh generation can be measured, the organizers of GMGW-1, with the assistance of the organizers of HiLiftPW- 3, focused GMGW-1 on generation of meshes of the NASA High Lift Common Research Model (HL-CRM). Some of the generated meshes were provided for use by the participants in HiLiftPW-3. All meshes and the processes by which they were generated were analyzed by GMGW-1 as a first assessment of state of the art practices. The results of GMGW-1 added quantitative detail to known problem areas including geometry modeling, data interoperability, and amount of human intervention. They do provide a clear path toward a vision of geometry preprocessing and mesh generation in the year 2030. The next milepost along this path will be a second workshop.

Computer numerical simulation is a beneficial tool for studying various domains of knowledge. Among the steps in the whole process of numerical simulation is the generation of unstructured meshes. Since the unstructured meshes are usually generated using automatic software, the fundamental knowledge of the unstructured meshes is often neglected. This paper highlighted some useful insights into the unstructured meshes in numerical simulation for several application domains, such as the radiative heat transfer problem, ocean modelling and biomedical engineering. It also reviewed some fundamental concepts and frameworks for element generation in producing unstructured meshes, particularly the Delaunay triangulation and advancing front techniques.

Solving the Poisson equation on small aspect ratio domains using unstructured meshes

A novel appro ach for generating unstructured meshes using elliptic smoothing is presented. Like structured mesh generation methods, the approach begins with the construction of a computational mesh. The computational mesh is used to solve elliptic partial differential equations that control grid point distributions and improve mesh quality. Two types of elliptic partial differential equations are employed; modified linear -elastic theory and Winslow equation s, with or without forcing functions . Results are included to il lustrate the use of these methods for unstructured mesh generation, mesh boundary shape modification, mesh untangling and mesh movement.

A parallel unstructured mesh generation technique is proposed based on the built-in cyber-physical system (CPS) of Parallel Virtual Machine context. A static load-balancing strategy for computational domain decomposition is firstly presented in the paper. After dividing the whole computational domain into several sub-domains, unstructured grids are separately generated in each sub-domain using the advancing-front grid generation technique. Besides, for a dynamic load-balancing strategy, Lohner’s advancing front domain-splitting algorithm is improved to make the sub-grids and their boundaries more favorable for the grid generation. Moreover, a new optimization strategy of sub-domain’s boundary is simultaneously presented to smooth the boundaries and improve the quality of grids. Finally, conditions of receiving new points and elements are also developed during the grid generation in the sub-domain. Meanwhile, a new strategy of receiving new elements and refusing new points during the interface grid generation is proposed, which can save computational cost. A new parallel Laplacian smoother technique is implemented to generate high-quality mesh. Meshes for NACA0012 airfoil, cylinder, and multi-element airfoil are generated by the improved parallel algorithm using the static and dynamic load-balancing strategies. Some comparisons of parallel calculations are also made using the different number of processors in the tables.

Unstructured mesh generation from the Virtual Family models for whole body biomedical simulations

A new method of unstructured mesh generation is presented. The advancing front method and Delauney triangulation have been commonly applied to it. In the former method, interior mesh nodes are generated based on the nodes on boundaries and parameters defined by the user. Unsuitable setting of parameters, however, may lead to failure in mesh generation. On the other hand, the latter method can accomplish mesh generation without failure, though the user has to set all the nodes. The present method, based on Delauney triangulation, requires the user to set only a few nodes on boundaries, and the other mesh nodes are generated automatically according to the curvature or proximity of boundaries. The perfomance of the presented method is illustrated in a region with multiple bodies.

A new physically-based approach to unstructured mesh generation via Monte-Carlo simulation is proposed. Geometrical objects to be meshed are represented by systems of interacting particles with a given interaction potential. A new way of distributing nodes in complex domains is proposed based on a concept of dynamic equilibrium ensemble, which represents a liquid state of matter. The algorithm is simple, numerically stable and produces uniform node distributions in domains of complex geometries and different dimensions. Well-shaped triangles or tetrahedra can be created by connecting a set of uniformly-spaced nodes. The proposed method has many advantages and potential applications.;The new method is applied to the problem of meshing of voxel-based objects. By customizing system potential energy function to reflect surface features, particles can be distributed into desired locations, such as sharp corners and edges. Feature-preserved surface mesh can then be constructed by connecting the node set.;A heuristic algorithm using an advancing front approach is proposed to generate triangulated surface meshes on voxel-based objects. The resultant surface meshes do not inherit the anisotropy of the underlying hexagonal grid. However, the important surface features, such as edges and corners may not be preserved in the mesh.;To overcome this problem, surface features such as edges, corners need to be detected. A new approach of edge capturing is proposed and demonstrated. The approach is based on a Laplace solver with incomplete Jacobi iterations, and as such is very simple and efficient. This edge capturing approach combined with the mesh generation methods above forms a simple and robust technique of unstructured mesh generation on voxel-based objects.;A graphical user interface (GUI) capable of complex geometric design and remote simulation control was implemented. The GUI was used in simulations of large fuel-cell stacks. It enables one to setup, run and monitor simulations remotely through secure shell (SSH2) connections. A voxel-based 3D geometrical modeling module is built along with the GUI. The flexibility of voxel-based geometry representation enables one to use this technique for both geometric design and visualization of volume data.

The volume of fluid (VoF) method is widely used in multi-phase flow simulations to track and locate the interface between two immiscible fluids. A major bottleneck of the VoF method is the interface reconstruction step due to its high computational cost and low accuracy on unstructured grids. We propose a machine learning enhanced VoF method based on Graph Neural Networks (GNN) to accelerate the interface reconstruction on general unstructured meshes. We first develop a methodology to generate a synthetic dataset based on paraboloid surfaces discretized on unstructured meshes. We then train a GNN based model and perform generalization tests. Our results demonstrate the efficiency of a GNN based approach for interface reconstruction in multi-phase flow simulations in the industrial context.

Implementation of a feature-constraint mesh generation algorithm within a GIS

A method of efficiently computing turbulent compressible flow over complex two‐dimensional configurations is presented. The method makes use of fully unstructured meshes throughout the entire flow field, thus enabling the treatment of arbitrarily complex geometries and the use of adaptive meshing techniques throughout both viscous and inviscid regions of the flow field. Mesh generation is based on a locally mapped Delaunay technique in order to generate unstructured meshes with highly stretched elements in the viscous regions. The flow equations are discretized using a finite element Navier‐Stokes solver, and rapid convergence to steady state is achieved using an unstructured multigrid algorithm. Turbulence modelling is performed using an inexpensive algebraic model, implemented for use on unstructured and adaptive meshes. Compressible turbulent flow solutions about multiple‐element aerofoil geometries are computed and compared with experimental data.

An adaptive finite element procedure is presented for improving the quality of solutions to convection‐dominated problems in geodynamics. The method adapts the mesh automatically around regions of high solution gradient, yielding enhanced resolution of the associated flow features. The approach requires the coupling of an automatic mesh generator, a finite element flow solver, and an error estimator. In this study, the procedure is implemented in conjunction with the well‐known geodynamical finite element code ConMan. An unstructured quadrilateral mesh generator is utilized, with mesh adaptation accomplished through regeneration. This regeneration employs information provided by an interpolation‐based local error estimator, obtained from the computed solution on an existing mesh. The technique is validated by solving thermal and thermochemical problems with well‐established benchmark solutions. In a purely thermal context, results illustrate that the method is highly successful, improving solution accuracy while increasing computational efficiency. For thermochemical simulations the same conclusions can be drawn. However, results also demonstrate that the grid‐based methods employed for simulating the compositional field are not competitive with the other methods (tracer particle and marker chain) currently employed in this field, even at the higher spatial resolutions allowed by the adaptive grid strategies.

An unstructured hierarchical mesh generation method is presented that uses multi-block structured meshes for construction. The structured blocks provide a scaffolding structure in a computational space that is used by a Cartesian-aligned hierarchical subdivision method for the generation of a hexahedral unstructured mesh. The structured blocks also provide a mechanism to transform geometry and mesh data from physical space to computational space and back. The strengths of the Cartesian aligned mesh generation method are fully realized in the transformed space. Feature based mesh adaptation is performed for inviscid and viscous cases. Results for several inviscid and viscous cases are included.

Subsurface reservoir models have a high degree of uncertainty regarding reservoir geometry and structure. A range of conceptual models should therefore be generated to explore how fluids-in-place, reservoir dynamics, and development decisions are affected by such uncertainty. The rapid reservoir modelling (RRM) workflow has been developed to prototype reservoir models across scales and test their dynamic behaviour. RRM complements existing workflows in that conceptual models can be prototyped, explored, compared, and ranked rapidly prior to detailed reservoir modelling. Reservoir geology is sketched in 2D with geological operators and translated in real-time into geologically correct 3D models. Flow diagnostics provide quantitative information for these reservoir model prototypes about their static and dynamic behaviours. A tracing algorithm is reviewed and implemented to compute time-of-flight and tracer concentrations efficiently on unstructured grids. Numerical well testing (NWT) is adopted in RRM to further interrogate the reservoir model. A new edge-based fast marching method is developed and implemented to solve the diffusive time-of-flight for approximating pressure transients efficiently on unstructured tetrahedral meshes. We demonstrate that an implementation of the workflow consisting of integrated sketch-based interface modelling, unstructured mesh generation, flow diagnostics, and numerical well testing is possible.