Computational Fluid Dynamics Blogs

Introduction

Despite the evolution of computer processing capability, improving the efficiency of numerical simulations remains critical. In CFD simulations, the key factor impacting solution quality is meshing. A mesh spacing that does not resolve local variations in the flow variables introduces a discretization error. On the other hand, if the mesh is overly refined, the computational time and effort are needlessly increased. Mesh element types and data structures also impact the human hours and skills required to generate a mesh and the cost per unit of accuracy.

Figure 1. Comparison between Local Error-based and Output-based Adaptation Technology.

Mesh adaptation (which can be local error-based or output-based), as depicted in Figure 1, is a common technique employed to help improve simulation efficiency. Unstructured mesh adaptation has been used to reduce the mesh size to reach the desired solution accuracy. This technique enables significant improvements in processing time, memory requirements, and storage needed. However, without access to the underlying CAD data, adaptation is limited only to improving off-body grid resolution. While the mesh adaptation technique in Fidelity CFD respects the geometry, improves the mesh quality, adapts to the near-wall shear layers, and reduces run-time for improved CFD solutions.

Challenges 

Usual challenges using mesh adaptation for improved mesh quality are as follows:

• Adaptation does not resolve the correct geometry. Most adaptation procedures are built into the CFD solver. Hence, they adapt only to a faceted approximation of the actual geometry (i.e., the existing geometry). After adaptation, one has the ideal mesh for the wrong geometry.
• Adaptation decreases the mesh quality of the locally refined mesh. Many adaptation procedures use a divide-and-conquer approach to enrich the mesh, whereby an existing mesh element is locally divided into additional elements. While convenient to program, this approach can lead to a steady decrease in mesh quality with refinement, reducing the robustness, increasing the run time, and perhaps even increasing the discretization
• Adaptation in near-wall shear layers where the gradients of the flow variables are extensive has many challenges. Brute force approaches typically use isotropic refinement near walls, causing an explosion in the mesh size. A common strategy to avoid the mesh size explosion employs stretched tetrahedra to resolve the large gradients normal to walls without over­-refining parallel to the wall. However, this approach leads to a massive decrease in mesh quality.
• Adaptation procedures often lead to excessive run times. This is because the mesh was either over-refined in some direction or location, or the mesh quality decreased during adaptation causing the CFD solver to struggle, or even the simple issue of when to stop the refinement procedure.

User Benefits of Fidelity CFD Meshing 

Fidelity Pointwise is a mesh generation solution that offers ample flexibility in mesh construction techniques and mesh styles. This flexibility is the meshing philosophy of the Fidelity CFD meshing tool and allows it to be applied to a wide range of workflows. The Pointwise mesh adaptation technology separates the meshing and solving steps in a coordinated and automated manner enabling refinement of the mesh as per the developing flow solution or based on the objective of the application (as shown in Figure. 2)

Figure 2. Mesh adaptation of a diamond airfoil for two different objectives, i.e., adapted for drag (left) and adapted for shock propagation (right).

This automatic mesh refinement tool is used only in those regions where the mesh is deficient. It starts by creating a baseline flow solution, and by using this flow solution, an estimate of the error corresponding to the deficiencies in the mesh size is determined. This step is repeated quite a few times to get a better hold of the mesh discretization error. For high-quality CFD meshing, this method can also be used on off-body voxel meshing for uniform and excellent resolution of the off-body features, specially to capture the wake region. In Figure 3, the wake shear layer mesh for the sedan is refined using the mesh adaption tool.

Figure 3. Mesh refinement to define off-body features.

Take-Away

The Fidelity Pointwise mesh adaptation tool

• Adapts to the underlying geometry.
• Efficiently resolves the mesh within boundary layer regions.
• Effectively controls the rate of adaptation, successively improving the mesh quality.
• Reduces run-time

To learn more about mesh adaptation in Pointwise, request a free trial license.