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Take the Mesh Defaults, or Not? That is the Question

Default Mesh | CFD Analysis
June 12, 2015 By: Hsin-Hua Tsuei

Recent developments in meshing technology for CFD analysis has made the meshing process much more convenient and easier to use. Generally speaking, a wide variety of CFD meshing methods and mesh element types are available to tackle complex geometry and challenging physics that require extensive mesh resolutions. To emphasize the ease of use, many codes offer a “default” mesh feature, where the mesher makes use of the surface and volume mesh sizes, curvature resolution, etc. to generate a mesh of the geometry of interest.  This default mesh generally only requires a few clicks to generate the mesh. The user has little control of the mesh element type and total element count if the default meshing process is implemented.  For a geometry with similar topology on two ends, or all faces, a good mesher will likely produce a mesh consisting of all hexahedron elements.  However, with a more complex geometry, the default 3-D mesh will often resort to tetrahedron elements.

The question then arises: Is the default mesh good enough? Should we all save valuable engineering time and just use the default mesh instead of spending hours, if not days, trying to refine a mesh? Let’s take a look at this simple example.  Figure 1 shows a heat sink used to dissipate 40 W of heat. The geometry is provided by the manufacturer and the dominant mechanism of heat transfer in this case is natural convection.
 

Figure 1: Heat Sink Geometry

The flow domain for the heat sink is shown in Figure 2, with the heat sink placed in the middle of an ambient domain.  For this CFD analysis, both the solid (heat sink) and the flow domain are meshed. In Figure 3, we used a “default” mesh, which uses the heat sink dimensions and geometry features, such as gap, curvature, and proximity, to determine element size and placement. The resultant temperature contours are superimposed on the mesh in Figure 3. 

Figure 2. Heat Sink Flow & Solid Domains

In this example, it became obvious that there was a problem because the solver diverged by using this mesh. The result shown in Figure 3 is obtained prior to the solver divergence. Clearly the default mesh, which has a total element count about 0.5 M elements, is not suitable to resolve this particular free convection simulation.

Figure 3: Default Mesh

Upon close examination, there are only two or three elements across each fin gap, which are not sufficient to resolve the temperature gradient near each fin (where heat is dissipated), and across the gap. It is apparent there are no prism layers near solid surfaces in the default mesh, which in this case, are critical to resolve the thermal gradient near each fin surface. If we simply place prism elements next to each fin surface with a total element count about 1 M, a converged solution is easily obtained.  That result is shown in Figure 4. Further mesh refinement to a total of 3M elements shows a similar thermal gradient and temperature profiles. The result is shown in Figure 5. (Note: in this example, the mesh element type has been maintained for comparison purposes.) 

Figure 4: Intermediate Mesh

The refined meshes, although not the default, took very little extra work to create. But, they did require a conscious effort on the part of the engineer to realize the original mesh was not appropriate and to take the proper steps to correct the problem. So, as with most engineering solutions, it comes down to a matter of understanding the physics, training, and experience in the use of the tools.

Figure 5: Fine Mesh | CFD Analysis

Now let’s see how these results stack up against test data. Table 1 shows the comparison. The test data is measured at a point on the heat sink surface, which is approximately 71°C above the ambient temperature. The default mesh result shows a much higher temperature prior to solver divergence.  With a bit more work (a few more clicks compared to using the default mesh), to get a better mesh, we can capture the temperature rise to within 1°C of the test data easily.

Therefore, this example shows us that relying on the default mesh may not always be a good thing, as sometimes the results can be a bit misleading.  The adequacy of a default mesh depends on the heuristic scheme used, along with the geometry and physics which must be resolved. The default may be perfect for one case, but not adequate for another. Perhaps one day, automated meshers will have built-in intelligence to produce perfect meshes every time without the engineer’s intervention, but that is not the state-of-the-art today, regardless of what the marketing material says. So after you right click to generate a default mesh, it is essential to review what the resulting mesh looks like, think about the flow physics associated with the project you are working on, stop for a minute, and ask the question:  Is the default mesh good enough? If you are not sure, refine the mesh and run again. Repeat until you have a converged answer.

I’m curious to hear about others’ experience with default meshing algorithms, so please post a comment if you would like to share your thoughts.