JIGSAW-GEO (1.0): locally orthogonal staggered unstructured grid generation for general circulation modelling on the sphere

An algorithm for the generation of non-uniform, locally-orthogonal staggered unstructured spheroidal grids is described. This technique is designed to generate very high-quality staggered Voronoi/Delaunay meshes appropriate for general circulation modelling on the sphere, including applications to atmospheric simulation, ocean-modelling and numerical weather prediction. Using a recently developed Frontal-Delaunay refinement technique, a method for the construction of high-quality unstructured spheroidal Delaunay triangulations is introduced. A locally-orthogonal polygonal grid, derived from the associated Voronoi diagram, is computed as the staggered dual. It is shown that use of the Frontal-Delaunay refinement technique allows for the generation of very high-quality unstructured triangulations, satisfying a-priori bounds on element size and shape. Grid-quality is further improved through the application of hill-climbing type optimisation techniques. Overall, the algorithm is shown to produce grids with very high element quality and smooth grading characteristics, while imposing relatively low computational expense. A selection of uniform and non-uniform spheroidal grids appropriate for high-resolution, multi-scale general circulation modelling are presented. These grids are shown to satisfy the geometric constraints associated with contemporary unstructured C-grid type finite-volume models, including the Model for Prediction Across Scales (MPAS-O). The use of user-defined mesh-spacing functions to generate smoothly graded, non-uniform grids for multi-resolution type studies is discussed in detail.Comment: Final revisions, as per: Engwirda, D.: JIGSAW-GEO (1.0): locally orthogonal staggered unstructured grid generation for general circulation modelling on the sphere, Geosci. Model Dev., 10, 2117-2140, https://doi.org/10.5194/gmd-10-2117-2017, 201

Geometry Modeling for Unstructured Mesh Adaptation

The quantification and control of discretization error is critical to obtaining reliable simulation results. Adaptive mesh techniques have the potential to automate discretization error control, but have made limited impact on production analysis workflow. Recent progress has matured a number of independent implementations of flow solvers, error estimation methods, and anisotropic mesh adaptation mechanics. However, the poor integration of initial mesh generation and adaptive mesh mechanics to typical sources of geometry has hindered adoption of adaptive mesh techniques, where these geometries are often created in Mechanical Computer- Aided Design (MCAD) systems. The difficulty of this coupling is compounded by two factors: the inherent complexity of the model (e.g., large range of scales, bodies in proximity, details not required for analysis) and unintended geometry construction artifacts (e.g., translation, uneven parameterization, degeneracy, self-intersection, sliver faces, gaps, large tolerances be- tween topological elements, local high curvature to enforce continuity). Manual preparation of geometry is commonly employed to enable fixed-grid and adaptive-grid workflows by reducing the severity and negative impacts of these construction artifacts, but manual process interaction inhibits workflow automation. Techniques to permit the use of complex geometry models and reduce the impact of geometry construction artifacts on unstructured grid workflows are models from the AIAA Sonic Boom and High Lift Prediction are shown to demonstrate the utility of the current approach

An insight into the science of unstructured meshes in computer numerical simulation

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

On the numerical convergence properties of the calculation of the flow around the KVLCC2 tanker in unstructured grids

This paper addresses the estimation of numerical errors in the calculation of the flow around the KVLCC2 tanker at model scale Reynolds number in unstructured grids. The flow solution is based on the Reynolds-Averaged Navier-Stokes equations supplemented by the k − ω SST two-equation eddy-viscosity model using the so-called double-body approach, i.e. free surface effects are neglected. Grid refinement studies are performed for sets of grids gener- ated with the open source code SnappyHexMesh and with the HEXPRESSTM grid generator. Definition of grid refinement ratio in unstructured grids and its consequences for the estima- tion of numerical errors is discussed. Friction and pressure resistance coefficients and mean velocity components at the propeller plane are compared with reference solutions obtained in nearly-orthogonal multi-block structured grids with the same flow solver ReFRESCO

Sketch-To-Solution: An Exploration of Viscous CFD with Automatic Grids

Numerical simulation of the Reynolds-averaged NavierStokes (RANS) equations has become a critical tool for the design of aerospace vehicles. However, the issues that affect the grid convergence of three dimensional RANS solutions are not completely understood, as documented in the AIAA Drag Prediction Workshop series. Grid adaption methods have the potential for increasing the automation and discretization error control of RANS solutions to impact the aerospace design and certification process. The realization of the CFD Vision 2030 Study includes automated management of errors and uncertainties of physics-based, predictive modeling that can set the stage for ensuring a vehicle is in compliance with a regulation or specification by using analysis without demonstration in flight test (i.e., certification or qualification by analysis). For example, the Cart3D inviscid analysis package has automated Cartesian cut-cell gridding with output-based error control. Fueled by recent advances in the fields of anisotropic grid adaptation, error estimation, and geometry modeling, a similar work flow is explored for viscous CFD simulations; where a CFD application engineer provides geometry, boundary conditions, and flow parameters, and the sketch-to-solution process yields a CFD simulation through automatic, error-based, grid adaptation

Delaunay triangulation in computational fluid dynamics

AbstractA method, which utilises the Delaunay criterion, is described by which computational grids consisting of assemblies of triangles or tetrahedra can be constructed. An algorithm is briefly outlined to construct the triangulation and its dual, the Voronoi diagram. Issues related to how to construct boundary conforming grids from such a triangulation are addressed, and details are presented of how grid points within the domain can be generated automatically. The point generation algorithm utilises either the given boundary point distribution, or, for grid adaption, a background mesh. Computational aspects of constructing the triangulation in both 2 and 3 dimensions are covered. Examples of meshes and flow computations for a range of aerospace geometries are presented

Implicit time accurate solutions on unstructured dynamic grids

In this paper an unstructured multigrid algorithm is used as an iterative solution procedure for the discrete equations arising from an implicit time discretisation of the unsteady Euler equations on tetrahedral grids. To calculate unsteady flows due to oscillating boundaries, a novel grid movement algorithm is introduced, in which an elliptic equation with a nonlinear diffusion coefficient is used to define the displacement of interior grid nodes. This allows large grid displacements to be calculated in a single step. The multigrid technique uses a edge--collapsing algorithm to generate a sequence of grids, and a pseudo--timestepping smoother. On the coarser grids, no grid motion is used. Instead, surface normals are rotated consistently and transfer/interpolation weights are based on the time-averaged grid coordinates. A 2D NACA0012 test case is used to validate the program. 3D results are presented for the M6 wing and a full aircraft configuration

Aspects of Unstructured Grids and Finite-Volume Solvers for the Euler and Navier-Stokes Equations

One of the major achievements in engineering science has been the development of computer algorithms for solving nonlinear differential equations such as the Navier-Stokes equations. In the past, limited computer resources have motivated the development of efficient numerical schemes in computational fluid dynamics (CFD) utilizing structured meshes. The use of structured meshes greatly simplifies the implementation of CFD algorithms on conventional computers. Unstructured grids on the other hand offer an alternative to modeling complex geometries. Unstructured meshes have irregular connectivity and usually contain combinations of triangles, quadrilaterals, tetrahedra, and hexahedra. The generation and use of unstructured grids poses new challenges in CFD. The purpose of this note is to present recent developments in the unstructured grid generation and flow solution technology