The fine folks at Mentor Graphics publish a lot of good white papers. One of their recent ones is is How to Choose an Effective Grid System for CFD Meshing.
I think it’s mis-titled. The paper should be called Why Cartesian Grids are Good. They actually undersell the benefits of Cartesian grids. They can be extremely useful in a variety of situations. (Keep in mind that Pointwise doesn’t generate Cartesian grids so I don’t have any stake in this game.)
The Case I’d Make for Cartesian Grids
- Compared to body-fitted grids, generating a Cartesian grid is trivial. And that’s a person’s time you’re saving.
- The price you pay for that triviality is complexity in how the boundaries are treated (i.e. cut cells). But that complexity is handled by the solver. Understand its limitations and you’re golden.
- Solutions on Cartesian grids tend to converge better than those of body-fitted methods.
- Other practitioners have been very successful with Cartesian methods.
What the White Paper Actually Says
“A Cartesian grid is the most common such system in practical use…” I take this to mean that the majority of all CFD analyses performed in the world today use Cartesian grids. This doesn’t jive with my personal experience but because I don’t claim to be omnipresent I’d like to see the data.
With respect to the issue of grid quality, “The velocity components solved for are almost always those aligned in the Cartesian coordinates directions.” In other words, you’re solving for Vx, Vy, and Vz so why not use an x-y-z aligned grid. Other than seeming like a bit of circular reasoning, I think that in reality what we want is grid alignment with the local flow direction, not the coordinate system in which the Navier-Stokes equations are derived.
The grid quality issue that’s undersold is how Cartesian systems don’t require additional numerics to account for a cell’s non-orthogonality. Boundary-fitted systems need additional terms to correct the diffusion flux and these additional terms have a tendency to make the system of equations “stiffer” and impede convergence of the solution. In other words, solutions on Cartesian grids converge better.
Representing complex geometry boils down to the matter of cut cells where the geometry passes through the Cartesian grid. The advantage cited is “Good grid quality is ensured, with the benefits explained earlier.” Nothing is farther from the truth. Cut cells are to Cartesian grids what hole cutting is to overset meshing – a gray area of black magic. That doesn’t make it a drawback, just something that should be addressed explicitly.
Certainly you can point to the work of Patankar, Spalding, Aftosmis, and Dawes as examples of good CFD with Cartesian grids but you have to make sure you’re comparing apples to apples. Aftosmis’ Cart3D is inviscid so you can’t make too general a conclusion about “the Cartesian-grid results are of comparable quality with results from body-fitted and more-complex grid systems.” Certainly that’s true in many cases but perhaps not all. (Aftosmis’ Cart3D is a superb example of the great things that can be accomplished with Cartesian mesh-based CFD – and I’m not just saying that because he’s a fellow Syracuse alum.)
Choosing Your Grid System
You really ought to checkout Mentor Graphic’s white paper and if it the benefits of Cartesian grid-based CFD resonate with you give them a call to find out more about their CFD software.
On the other hand, if your CFD solver of choice doesn’t support Cartesian grids perhaps you should take a look at Pointwise for your multi-block, structured hex, unstructured tet, and hybrid meshing.