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Meshing is the process of dividing up the domain of interest into smaller elements (or cells) so that numerical methods can be used to solve the partial differential equations required to model fluids. Creating a high quality mesh is crucial for obtaining accurate results, plus it often helps the simulation converge faster. This guide will focus more on how to setup a mesh in SimScale but I’ll start with a brief discussion on mesh design to provide context for the various settings.

Mesh Design

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Mesh design is mostly about finding just enough mesh elements to accurately represent the geometry of interest. Minimizing the number of mesh elements reduces the time and computing power required for the simulation, but not having enough increases the error of the results. A simplified quick metric to use is the total number of elements. This number gives a rough idea of the mesh resolution and can help predict how long a simulation will take, or if SimScale can even complete the simulation. What I mean by this is that after about 12-14M elements, SimScale will run out of memory when using 16 cores. For reference, we mostly used 10-12M elements during the development of MSXIV.

First, the region that will be simulated must be determined. This is known as the Background Mesh Box (in SimScale, it is also Also commonly called the bounding box or domain). Typical guidelines are to use 2-8 times the car’s dimensions as the dimensions of the domain. Less space is needed on the sides, a moderate volume space is needed in front of the car, and the majority of space should be behind the car. So for MSXIV (Approximately 5 m long, 2 m wide, 1 m tall), the domain should extend about 15 -20 m (= 5 m * 3 or 4) were created in front of the car, 35 -40 m (= 5 m * 7 or 8) behind the car, and 4- 5 m above and on either side. This results in a domain that is 50 m long, 10 m wide, and 5 m tall. Now, it is important to note that there is a plane of symmetry running down the center of the car (I guess this isn’t necessarily true for all cars but for most cars it is). This means that we only need to simulate half of the car. The resulting drag (and other forces) can be doubled when post-processing, since each half of the car should have identical drags. This can drastically reduce the number of elements in your mesh, without sacrificing resolution and is something we did not take advantage of for the design of MSXIV. For example, the 12M element meshes we used could have been recreated to the same resolution by using a 6M element “half-mesh”. Or, more importantly, the accuracy of the simulation could be improved by using a half-mesh with 7-9M elements (equivalent to 14-18M elements of a full mesh) and SimScale will have enough memory even on 16 cores. The end result is a domain that is still 50 m long and , 5 m tall, but only and 5 m wide, offset to one side of the car.

Once the size of the domain is determined, the resolution on the surface of the car must be decided upon. This is partially determined by how the boundary layer will be modelled. There are 2 strategies for this: using full resolution or using wall functions. Whichever strategy is chosen will determine the height of the boundary layer elements in the direction perpendicular to the surface. The lateral dimensions of the elements should be close similar in value to the height.

Then refinements should be are used to create appropriately sized elements between the car’s surface and the domain walls. Essentially, the area around the car should have the finest elements, then the edges of the domain should have the coarsest elements, and there should be a gradient of element sizes between them. There should also be moderately fine elements in the wake of the vehicle.

Mesh Settings

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General Mesh Settings + Geometry Primitives

I think that gives enough context to start, so I’ll talk about how to actually set this up in SimScale now. To start editing the mesh settings, click Mesh in the left navigation panel.

General Mesh Settings + Geometry Primitives

That should bring up global mesh settings, meaning that these settings apply everywhere in the domain (Other settings may only apply to specific regions). Change the algorithm from Standard to Hex-dominant parametric. This gives more control over the mesh and primarily uses hex-based elements rather than tet-based elements. Now expand the Geometry primitives section in the navigation panel and select the Background Mesh Box. A panel should open with the minimum x, y, and z coordinates, along with the maximum x, y, and z coordinates. I used minimum values of 0, 0, and -35, and maximum values of 5, 5, and 15. Next, select the Material Point section. This point determines which volume is divided into elements, so make sure the point is located within the background mesh box, but outside of the car geometry. While we’re here, add 2 Cartesian box geometry primitives. Select a region trailing from the car with one box inside the other one. For example use 0, 0, -20 to 2, 2, -4 for one, and 0, 0, -16 to 1.5, 1.5, -4 for the other. This is to enclose the wake behind the car, with 2 different mesh densities. Return to the general mesh settings. Beneath the algorithm setting, there should be a section for Bounding box resolution. I’ve been using values of 20, 20, and 200.

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Using a mesh that is 20x20x200 is not fine enough to represent the flow patterns around a vehicle . This is why refinements existso refinements will be added around the car. Locate the Refinements section in the navigation panel, and begin by adding a bounding box refinement. Change the Face to Ymin, Min thickness to 0 m, and Final thickness to 12e-3 m. Save the refinement by clicking the blue check mark in the top right of that panel. Add a region refinement. Change the Refinement mode to Distance and use values similar to those from Table 2.1. These values can vary depending on how many elements you want in your mesh.

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Assign this refinement to the car geometry by clicking the car in the geometry viewer (you may need to click inside the box that says Pick Volumes first so that the program knows you’re ready to select the geometry, ensure the box is blue). Add 2 more geometry refinements, this time leave the modes as Inside. Set the level of the first one to 2, and assign it to the larger Cartesian box geometry primitive that was created earlier by clicking the sliding switch to the left of the label at the bottom of the panel. Then set the level of the second one to 3 and assign it to the smaller Cartesian box geometry primitive that was created earlier. The next refinement is called a Surface refinement. I started using it because I find it helps with the step afterwards (forming the boundary layers). Set the Min level and Max level to 5 and assign it to the car entity. We don’t need cell zones for this type of simulation.

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The last refinement we need is a boundary layer refinement. This allows the simulation to properly model the effects of the boundary layer on the airflow around the vehicle. Add the Inflate boundary layer refinement and set the layers, expansion ratio, min thickness, and inner layer thickness to the desired values, based on whether you want to use wall functions or full resolution. I would start with wall functions, as they are computationally cheaper and I’ve had slightly better convergence with them. I have been I’ve had success using 10 layers, at an expansion ratio of 1.2, a minimum thickness of 0 m, and an inner layer thickness of 6.6e-3 m. Select all the faces of the vehicle.

Those are all the refinements that I generally use, however the problem is that if this mesh is generated now the boundary layers will be missing. Maybe not all of them, but the vast majority in my experience. Proper boundary layer modelling is critical for predicting boundary layer separation, which can lead to massive increases in drag. This means we need to find out why the boundary layers are not being formed and then correct this if we want to accurately predict the drag of our vehicle. Why this happens is likely quite complicated and influenced by many factors. My understanding fluid behaviour around the vehicle so this must be corrected. My understanding of why this happens is that all of the layers are actually formed as requested during mesh generation but many of these layer elements do not meet quality standards and are removed. The solution is to either create higher quality layer elements or to relax the quality parameters, allowing lower quality elements to be used. Both of these require the advanced settings section I mentioned earlier (Return to Mesh in the navigation panel and scroll down to find the advanced settings).

Scroll down until the Snap controls, change the settings indicated in Table 2.2, then scroll to the Layer adding controls. Change the following settings indicated in , and make the changes indicated in Table 2.3:

Table 2.2: Snap controls

Table 2.23: Advanced layer addition settings.

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These changes are mostly to allow more iterations to develop high quality layer elements, with the exception of the last onegenerate the layer elements so that they are of higher quality. A few of these settings also speed up the mesh generation process. Then scroll down to Mesh quality controls and make the changes indicated in Table 2.34:

Table 2.34: Mesh quality settings.

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You can now hit the Generate button in the bottom right of the settings panel.

Reviewing the Mesh

After the mesh has been generated, navigate to mesh and click the yellow button that appears to select the mesh as your domain. The icon besides Mesh in the navigation panel should change from yellow to green. Before proceeding, we should check to make sure it looks right and that no mistakes have been made. SimScale has several tools for this, some of which have been recently added after MSXIV’s aerobody design was locked. The first and most basic is the mesh element count, found in the general mesh settings under Mesh selection. If your mesh is way smaller or way larger than expected, something may be wrong and any issues should be addressed before moving onto the simulation. The next quick check is to scroll down to the bottom of the Mesh quality controls and expand the new section called Event log. This section has element counts for each type of element. I believe the Number of prisms refers to the number of layer cells and can be used in the same way as the total element count. Fewer prisms than usual can indicate that too many layers were removed, which should be inspected and addressed before continuing. I was able to get around 22k prisms for wall function meshes. A more detailed inspection can be done by looking at the mesh in the 3-D display. The symmetry plane provides a convenient cross-section to look at the boundary layers running along the middle of the car, and the mesh clip tool can be used to create any other cross-sections. Finally, you can navigate to the Mesh quality section to conduct more detailed and quantifiable analysis of your mesh quality, although it does take a while to load.

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title Mesh Results
Figure 2.1: Symmetry plane of the mesh generated by the discussed settings. Figure 2.2: Closer view of the boundary layer elements around the front of the vehicle. Figure 2.3: Closer view of the boundary layer elements around the pontoon, created with a mesh clip.

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title Bad Mesh Results
Warning Figure 2.4: Incomplete boundary layer formation around the pontoon, notice the discontinuous boundary layers and wavy distortions that are created outside of the prism elements.

You may also have noticed a section called Meshing log, this can be used to see what the mesh generation algorithm is doing while the mesh is being generated. I would consider this to be an advanced tool, but it can be useful for troubleshooting problems. For example, this is the main tool I used to identify which of the advanced mesh settings needed to be changed to retain more boundary layersThis can be difficult to read at first, but it does provide a lot of information about the mesh.

If the mesh is an appropriate size, with an appropriate number of boundary layer cells, and no obvious defects you can continue to the actual simulation.

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