CFD meshing applies a numerical grid to a fluid body and boundary, similar to meshing in finite element simulations.
Meshing algorithms are used to generate collections of grid points, which will determine the accuracy of a CFD simulation.
There is a tradeoff between grid density, solution accuracy, and computation time. CFD simulations need to balance solution accuracy and computation time by adjusting the mesh density.
When you need to solve a differential equation or a system of differential equations, it’s often the case that a numerical technique is used. Flows in systems with simple geometry can sometimes be solved by hand, but even simple flows in complex geometries require numerical solution methods. With these numerical methods comes the need to define a grid of points in space and time to define the solution space for the problem at hand.
One of the challenges in fluid dynamics problems is to select a solution method and implement an appropriate CFD meshing method to expedite the simulation. In this article, we’ll examine how meshing techniques are used in CFD simulations as well as what to expect from CFD meshing features in commercial simulation packages.
What to Expect From CFD Meshing Methods
All CFD meshing methods have the same high-level objective: to create a grid of points that are used to solve the system of partial differential equations that govern fluid behavior in a CFD simulation. The geometric mesh used in a given CFD problem can be rather complex, as shown in the example below. The geometry formed by the mesh points (tessellations, tetrahedra, trapezoids, hexagons, etc.) can also shift between different regions of the system while also having a varying density across the structure.
Example mesh applied to turbine blades
Different CFD simulation software packages will use various algorithms for generating a set of mesh points along the structure to be simulated. Mesh points can be applied along a surface in three dimensions as well as within a 3D volume (i.e., volumetric mesh). As the density of mesh points increases, the accuracy of the solution within a given region of the system will also increase, just as is the case in multiphysics problems or mechanical problems.
The two considerations in applying CFD meshing are as follows:
- Mesh density: The density of grid points in the mesh will depend on the solution gradient in the system. In CFD problems, regions with high flow velocity gradient or in boundary layers near curved surfaces are good candidates for higher mesh density, as these regions may require higher accuracy.
- Mesh geometry: As was mentioned above, the mesh points can be connected to define cells that are hexahedra, tetrahedra, or even more complex tessellations.
The first point is quite important in modern CFD techniques, as the mesh density is set dynamically, known as adaptive meshing. The density of the mesh follows the physics and structure in the problem, as it depends on the flow gradient and the curvature in the problem, so it can be applied to naturally assure accuracy in critical areas.
There is certainly a tradeoff between accuracy and simulation time, both of which are determined by mesh density for a given type of mesh. Certain application areas might require very high accuracy and thus a higher mesh density in specific regions of the system. If we look at the highly curved portions of certain systems, such as the leading edge of an airfoil, we can see that gradient-guided meshes can be very dense in these regions, as the flow gradient can become very large in the approach to the surface. In other cases, multiple iterations might be used to explore variations on a structural design, so lower accuracy can be accepted. If the goal is to reduce the computation time for multiple design variations, then lower accuracy may be acceptable and a less dense mesh could be used.
Structured meshing (also known as mapped meshing) derives its name from the fact that the mesh points define an IxJ array of quadrilaterals (in 2D) and an IxJxK array hexahedra (in 3D). The structure is implicit because, at any mesh point, its neighbors are implicitly known. This structure adds efficiency to the mesh generation and flow solver algorithms. Structured meshes can be generated using a variety of well-defined mathematical techniques, ranging from algebraic to conformal mapping to the solution of partial differential equations. The structure required of a structured mesh makes them challenging to generate for complex shapes, and, in practice, usually involves a multi-zone technique where several structured grids are knitted together. In general, it is believed that CFD solutions computed on quad and hex structured grids are more accurate than other cell types.
Unstructured meshing typically refers to meshes that consist of triangles (in 2D) and tetrahedra (3D). Their unstructured nature (relative to structured meshes) comes from the fact that the neighbors of any grid point have to be determined explicitly through some form of look-up. The algorithms used to generate unstructured meshes are generally based on the Delaunay criterion or an advancing front technique. These methods are able to mesh with relative ease geometrically complex shapes. On the other hand, the accuracy of CFD simulations computed on pure unstructured meshes can be lower than the accuracy on structured grids due to the lack of alignment of the grid lines, especially in regions like the near-wall boundary layer.
To achieve the best of both worlds (accuracy and geometric flexibility), most modern CFD simulations use a hybrid mesh consisting of the cell types from structured and unstructured techniques (hexahedra and tetrahedra) combined with prisms and pyramids. More importantly, the near-wall mesh uses a semi-structured technique that creates layers of cells to resolve the boundary layer and then transitions to other cell types as the mesh moves away from the geometry model.
Example showing the effects of skewness in a CFD mesh
The suite of CFD meshing tools from Cadence like those in Pointwise are ideal for grid generation and defining meshes for use in CFD simulations with modern numerical approaches. In Cadence's simulation suite, our support for a variety of mesh types and techniques ensures you can generate the most suitable mesh for your application.