This presentation was held at the 2020 NAFEMS UK Conference "Inspiring Innovation through Engineering Simulation". The conference covered topics ranging from traditional FEA and CFD, to new and emerging areas including artificial intelligence, machine learning and EDA.

Resource Abstract

Demand continues to grow for robust and efficient automated numerical simulation pipelines. However, mesh generation remains a bottleneck, often requiring excessive human intervention. Progress continues to be made on robust, reliable unstructured mesh generators, but mesh sizing should not be overlooked as a critical component of the automatic meshing workflow.

Appropriate mesh sizing becomes particularly important as the limits of simulation fidelity and complexity are reached. Excessive mesh density may produce accurate results but at the expense of an impractical number of degrees of freedom, whereas coarse meshes may fail to capture necessary details and render the simulation irrelevant.

We have developed an extensive rule-based framework for automatic mesh sizing, where a series of rules can be combined into a single sizing field, which then drives intelligent element sizing during both mesh generation and smoothing operations.

On edges, the mesh sizing field is held as a graph of mesh density along the edge. For faces and volumes, the mesh density is held as a metric tensor over a triangular/tetrahedral scaffold. This allows anisotropic mesh densities to be easily represented and provides a straightforward interface to many metric-based mesh generators. Using these density-based methods provides a natural way to combine multiple sources of sizing data.

Typically, the first layer of sizing rules are geometric ones: SAG (elements must lie within a given distance of the geometry), TURN (maximum angle between neighbouring elements), and maximum and minimum element sizes. For the common case of isotropic meshing, edges are also sized using SCURV and STURN rules, which set sizing along an edge to meet sag and turn criteria in the transverse direction.

More sophisticated geometry-based sizing rules, such as proximity, can also be applied. A 2D medial axis analysis of model faces allows a density to be calculated along edges which will ensure a specific number of isotropic elements internally across a face.

User-driven or templated mesh sizing can be overlaid onto the sizing field. Mesh control sources are commonly used in aerospace CFD, and there are in-house tools available for generating templated sources for common configurations, providing sizing required to capture specific flow physics phenomena such as wakes. Source fields can be integrated with our sizing field to combine automated, templated and manual element sizing.

Further transformations can also be applied to the sizing field. A RATMAX rule ensures that adjacent elements satisfy a maximum size growth ratio. The ANIMAX rule enforces a maximum anisotropy within a face interior. The MATCH rule ensures that sizes are matched between neighbouring edges, faces, and volumes, allowing sizing for unstructured faces and volumes to match sizing imposed by neighbouring structured meshes.

Our sizing fields are constructed bottom-up: first a sizing field is built along edges, then we construct the field over faces, and finally we build a field in the volumes. The “back-propagation” of sizing from faces onto edges can also be employed, which allows dense sizing along one edge to propagate through the interior of a face, and affect the density on a neighbouring edge. This ensures successful generation of good quality meshes even when automatic sizing indicates rapid changes in mesh density.

We have implemented these mesh sizing techniques inside ITI’s CADfix solution. The sizing rule framework is respected by the edge, face, and volume mesh generators, including isotropic and anisotropic triangular mesh generators, an anisotropic quad-dominant mesh generator, and isotropic and anisotropic tetrahedral mesh generators. We will demonstrate how these methods have been successfully applied to the CFD meshing of industrial airframe configurations, and FEA meshing of industrial turbofan components.