Hy everybody, does anuyone know a method for generating a orthogonal mesh on a 3D curved surface. Thanks.

3D orthogonal coordinate systems do not exist in general. That is, your curved surface cannot, in general, be a constant coordinate surface of a 3D orthogonal coordinate system (although it can if your surface curves in only one direction?).

This raises two questions: where does the requirement for orthogonality come from? and what mathematical properties are actually required in the curved grid. Devising a method that directly seeks to minimise the required numerical property would seem the optimum way forward.

One simple approach to generating a reasonably "orthogonal" grid would be to solve the 2D orthogonal generating equations via projection onto the surface and evaluating the scale factors with 3D distances. I can think of a couple more approaches but hesitate to make a firm recommendation without having done it.

Actually, this has been done before by using Poisson equations for the grid lines. A description of this can be found in "A Fast Method for the Elliptic Generation of Three-Dimensional Grids with Full Boundary Control" by A. Hilgenstock. This was published in 'Proceeedings of the Numerical Grid Generation in Comp. Fluid Dynamics Conference', edited by S. Sengupta, 1988. A briefer description can also be found in "Numerical Methods for Engineers and Scientists", by J.D. Hoffman, McGraw-Hill, 1992.