# 3D Hyperbolic Grid Generation - Help Requested...

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 October 23, 2003, 23:24 3D Hyperbolic Grid Generation - Help Requested... #1 Marcus Lobbia Guest   Posts: n/a I'm currently developing an automated grid generation program for complex 3D configurations using overset grids (it will be generating grids for my 3D Euler/NS compressible flow solver). Anyway, I'm having some difficulties getting the 3D field grids generated using hyperbolic methods. [For reference, I'm attempting to code the algorithm from "Handbook of Grid Generation" pp. 5.3-5.10, and "Enhancements of a Three-Dimensional Hyperbolic Grid Generation Scheme" by Chan & Steger, App. Math. and Comp. Vol. 51 pp. 181-205]. I'm using a block tridiagonal solver to integrate the linearized system of equations. However, I'm having problems with stability (especially on highly-clustered surface grids). Any suggestions or comments from anyone with experience in developing these types of programs is appreciated. Also, if anyone can point me in the direction of some source code for setting up the block-tridiagonal system (or for the algorithm in general), I'd appreciate it - it might help me figure out some of the problems in my own code. Thanks in advance...

 November 8, 2003, 13:12 Re: 3D Hyperbolic Grid Generation - Help Requested #2 John Chawner Guest   Posts: n/a Hello, Marcus. We've worked in this area also. The good news is that the work of Chan & Steger is the best you can find on this topic. Chan's OVERGRID and HYPGEN programs are very, very good. Our Gridgen software may be the only implementation of the hyperbolic method in a commercial mesher and I was fortunate (?) enough to write the initial implementation many years ago. As you've found out, stability is the biggest problem with respect to the hyperbolic method. Balancing the implicit and explicit smoothing is key. But also, if you have concave regions you'll probably also need to implement the smoothing technique of Kinsey & Barth in addition to the method's built-in implicit and explicit smoothing. I can look up the K&B reference if you'd like. Another technique that comes in handy is something called volume smoothing. I don't recall who originally introduced this idea (it may have been Steger), but it slightly averages the volumes on each marching step so that you can dissipate clustering along the marching front as you march outward. This tends to improve stability by ensuring that your cells don't develop very high aspect ratios in the marching direction. Finally, a good source of a block tridiagonal algorithm (as long as you don't mind typing) is the classic CFD textbook by Anderson, Tannehill, and Pletcher - there's one in the appendix. I hope this helps.