Meshing

What is Meshing or Mesh Generation?

Meshing or mesh generation discretizes a geometry surface or volume into multiple elements. The required variables are calculated across these elements using partial differential equations. During meshing, the 2D surfaces are represented using a collection of triangles and quadrilaterals, while the 3D volumes are discretized into tetrahedrons, quadrilateral pyramids, triangular prisms, and hexahedrons.

Meshing is classified into three types:

1. Structured Meshing

A structured mesh has an underlying representation as a three-dimensional array, that is, a simple mapping from the (x,y,z) locations of the cell centers to (i,j,k) indices in arrays. Therefore, if we have the (i,j,k) index of a cell, we automatically know its neighbors are stored at (i±1,j±1,k±1). Structured meshes are particularly advantageous for high-speed simulations because the solver need not store neighbor cell lookup lists, which adds significant overhead.

Geometrically, structured meshes are limited to blocks of 2D quad or 3D hexahedral cells generated using various well-defined mathematical techniques, from algebraic to conformal mapping to solutions of partial differential equations. However, the geometric constraints of a structured mesh make them challenging to generate for complex shapes. Modern structured meshes are typically block-structured, consisting of multiple structured meshes stitched together. It is often observed that CFD solutions computed on quad and hex-structured grids are more accurate than other cell types.

2. Unstructured Meshing

An unstructured mesh is where the underlying representation includes a neighbor cell lookup list. Unstructured meshes are geometrically unconstrained and can include polygons (in 2D) or polyhedral (in 3D) with any number of faces and edges. Tetrahedral meshes generated by the Delaunay or advancing front methods are especially common. However, pure hexahedral meshes can still be unstructured, and it is formally incorrect to refer to them as “structured” if they lack an (i,j,k) representation. Unstructured meshes are popular in industrial CFD because they can be generated on geometrically complex shapes with relative ease. However, the resulting cells often have undesirable properties, such as high skewness and poor alignment, which can often degrade solver accuracy due to high truncation error and numerical diffusion.

3. Hybrid Meshing

To achieve an optimal combination of accuracy, speed, and flexibility, some modern CFD solvers use a hybrid mesh consisting of both structured blocks and unstructured regions and many different cell types. Typically, the near-wall mesh will use prism layers to resolve the boundary layer, which then transitions to other cell types as the mesh moves away from the geometry model.

 

Why is Meshing important?

The quality of a mesh (measured by geometric metrics for each cell in the mesh) influences the accuracy and convergence of the CFD solution. Achieving a balance between accuracy and computational resources is crucial to a good simulation, and mesh sensitivity tests are conducted to achieve this balance. For certain geometries, a coarse mesh suffices for the needs of the simulation. Therefore, the requirements of the CFD application determine the needed mesh quality and solution accuracy.

How to Generate High-Fidelity Mesh?

Meshing is the most time-intensive part of a CFD workflow and significantly impacts the simulation results. The following three steps can ensure a high-quality mesh generation process:

1. Geometry Clean-up and Watertight Geometry

Geometry cleanup can save simulation time and is a crucial step in CFD analysis, often taking days or even weeks, depending on the complexity of the geometry. A geometry devoid of unnecessary features, layers, and skins can provide a more accurate fluid flow solution. Further, a watertight geometry can help the solver simulate different flow domains.

2. Mesh Refinement in Regions where Physics is Crucial

A mesh spacing that does not resolve local variations in the flow variables introduces discretization error. However, if the mesh is overly refined, the computational time and effort increase needlessly. Hence, a suitable grid size must be chosen per the geometry and application. Mesh refinement is recommended to capture near-wall behavior and physics in the intricate geometry regions.

3. Mesh Convergence Study

A mesh convergence study is when the simulation is run on finer and finer meshes until flow quantities stop changing significantly. This typically needs to be done once for a new geometry to ensure the mesh is just fine enough to deliver a useful result, without making it so fine that computation time and memory requirements are excessive.

Meshing with Cadence

Cadence Fidelity Pointwise is a standalone CFD mesh generator providing the full range of functionality from geometry model preparation and mesh generation using various techniques to compatibility with a broad range of flow solvers. While generating a mesh, the lower-level entities glue the higher-level entities together to form a contiguous mesh, which allows much flexibility in mesh construction techniques and styles. This flexibility is the meshing philosophy of the Fidelity Pointwise product and enables its application to a wide range of workflows. Moreover, the mesh topology is independent of the CAD geometry and offers flexibility. The different meshing technologies in Fidelity Pointwise can address the grid discretization challenges in varied applications.

Fidelity Automesh technology automates the laborious geometry preparation process without losing any geometry detail and delivers quality meshes ready for CFD analysis in near real-time. The Fidelity Automesh solution combines different meshing techniques into a single workflow. Users can easily couple their flow solver into Fidelity meshing technology within the Fidelity environment and take advantage of a highly streamlined workflow.