Abstract: Mesh Adaptation, also known as Adaptive Grid Refinement (AGR), has long been used to modify an existing mesh to capture flow physics accurately. This method has several drawbacks, such as the inability to resolve the underlying geometry, excessive run times due to refinement, and decreased mesh quality. However, Fidelity Pointwise and ISimQ have developed a new mesh adaptation procedure that promises to address these challenges and automate the overall adaptation process. In this article, the mesh adaptation procedure is applied to the DrivAer model to study the efficacy of this adaption procedure in drag prediction for its use in commercial aero vehicle models.
Computational fluid dynamic (CFD) solutions enhance the product design process and help make reliable decisions that benefit the product. While it is “easy” to perform CFD simulations using commercial CFD software, the quality of the results remains squarely on the shoulders of the CFD analyst.
CFD simulation quality is often measured in terms of numerical, model, and systematic errors. Model errors originate from physical models such as turbulence, heat transfer, phase change, and chemical reactions. Systematic errors relate to differences between a device’s true and computer representation, such as the level of geometric detail and boundary conditions. Numerical errors refer to the discrete CFD solution of the governing conservation equations. They consist of discretization errors, iteration errors, and precision errors. In contrast to model and systematic errors, CFD analysts directly control numerical errors.
In CFD simulations, the most critical factor impacting solution quality is meshing. A mesh spacing that does not adequately resolve local variations in the flow variables introduces discretization errors (they are mesh-related); the flow equations are not accurately solved. On the other hand, if the mesh is overly refined, the computational time and effort increase needlessly. In a perfect world, a CFD mesh has elements with 90º between adjacent edges, a volume expansion ratio approaching unity, and a low mesh aspect ratio. In practice, all meshes fall short of “perfection.”
Mesh Adaptation Goals and Challenges
With mesh adaptation, a CFD simulation begins on an initial mesh and improves the mesh to reduce the discretization errors for the flow at hand. Initially, the adaptation algorithms estimate the truncation errors. Then, they enrich the mesh in the areas of the highest gradients, with efforts to reduce discretization errors and to determine the “ideal” mesh for the simulation problem. Adaptation sounds impressive and is also available in commercial CFD packages. Unfortunately, most mesh adaptation procedures negate the key benefits they are trying to address:
- Adaptation does not resolve the correct geometry. Most adaptation procedures are integral to the CFD solver. Hence, they adapt only to a faceted approximation of the actual geometry.
- Adaptation decreases mesh quality when locally refining the mesh. Many adaptation procedures use a divide-and-conquer approach to enrich the mesh. This approach can lead to a steady decrease in mesh quality with refinement, causing a decrease in robustness, longer run times, and perhaps even increased discretization error.
- Multiple challenges in adaptation in near-wall shear layers. Brute force approaches typically use isotropic refinement near walls, causing an explosion in the mesh size. A common strategy to avoid such mesh size explosion is to employ 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. Excessive run time is sometimes due to over-refinement in a certain direction or location. Suppose the computational effort associated with adaptation far outgrows a “standard” CFD simulation. In this case, analysts usually give up on adaptation and make the best mesh possible for the expected flow field within human time, computing time, and resource constraints.
A New Mesh Adaptation Procedure
In a joint effort, Pointwise and ISimQ have developed a new mesh adaptation procedure that addresses the above challenges. The adaptation procedure separates the meshing and solving steps in a coordinated and automated manner, managed by an overall adaptation program.
In the first step, the analyst creates an initial mesh to start the adaptation procedure. This initial mesh should adequately resolve the near-wall boundary layer regions and control the target near-wall distance, removing this task from the mesh adaptation procedure. After a first CFD simulation on the initial mesh, the adaptation algorithm extracts gradients of critical flow variables and calculates the sensor field.
Figure 1. Mesh element and mesh edges
The adaptation software calculates and forwards a point cloud target edge length to the Fidelity Pointwise meshing software and generates an improved mesh to achieve the desired local target edge length distribution. The adapted mesh preserves the initial user-defined mesh settings, and most importantly, the boundary layer meshing strategy. The adapted mesh inherently conforms to the underlying geometry known by the mesh generator. The mesh quality consistently improves with each mesh adaptation cycle, as the point cloud data consistently refine the mesh, and no a priori choice of a “local subdivision” is necessary. As a bonus, the adaptation process naturally identifies and corrects areas of large mesh expansion ratio.
The entire process is computationally efficient because the mesh is refined only in local areas. However, the restart process relies on a high-quality and automated interpolation procedure to map the previous solution onto the adapted mesh. This functionality is built-in into many CFD solvers. There is a “multigrid-like” effect, whereby the main flow features and the “hard work” to adjust the flow from the start occur with little computational effort with the coarser meshes. The adapted finer meshes require fewer CFD simulation iterations as the mesh changes are small at the end of the adaptation cycle.
Mesh Adaptation for AeroVehicle Application - DrivAer
Initially, Pointwise and ISimQ validated the adaptation method for turbomachinery flows. Here, the mesh adaptation technique is applied to an external aerodynamics problem. In 2011, the Technical University of Munich, Germany, introduced the generic DrivAer model to reduce the gap between simplified models and highly complex designs, as Figure 2 shows. This symmetrical closed car model has a fastback design, standard mirrors, a smooth underbody, generic rims, and no tire tread.
Figure 2. DrivAer geometry model
With the symmetry model, ISimQ only needed to simulate half of the geometry. The flow solver driving the adaptation was Ansys CFX. The effect of turbulence on the mean flow was modeled using the SST two-equation model. The initial mesh had 1.6 million nodes, and the final adapted mesh had 24.4 million nodes. Figure 3 illustrates the refinement of meshes at the start and end of the adaptation cycle.
Figure 3. Surface mesh after adaptation cycle 1 (left), surface mesh after adaptation cycle 6 (right)
Figure 4 shows the vortices behind the car for adaptation cycles 1 and 6, and Figure 5 demonstrates that the mesh adaptation procedure is geometry-sensitive. Unlike other adaptation schemes, the current method makes round surfaces “rounder” and conforms to the underlying geometry as the adaptation proceeds.
Figure 4. Vortex in the wake of the car after adaptation cycle 1 (left), vortex in the wake of the car after adaptation cycle 6 (right)
Figure 5. Mesh at the rear of the car after adaptation cycle 1 (left), mesh at the rear of the car after adaptation cycle 6 (right)
Figure 6 shows the variation of the drag force on the car as a function of the adaptation cycle. As the meshes become finer, the drag force asymptotes to a value around 68N.
Figure 6. Drag force as a function of the adaptation cycle
Fidelity Pointwise and ISimQ have developed a new mesh adaptation process that aims to achieve the long-standing hopes and promises of adaptation. The DrivAer model study confirms that this new mesh adaptation method can be successfully used for accurate drag predictions in aerovehicles. Further, the adaptation method confirms the underlying geometry as the adaptation proceeds, adjusts to the flow topology, and successively improves mesh quality, leading to a highly robust and efficient automated mesh adaptation procedure.
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- Galpin, Paul., Wyman, Nick., CFD and Mesh Adaptation – Aerodynamic Simulations.
- DrivAer Model. https://www.epc.ed.tum.de/en/aer/research-groups/automotive/drivaer/