Grid generation.
 

I'm developing 2-D structured multi-block quad mesh generating code with connectivity matrix using transfinite interpolation. Please suggest some good and relatively easy algorithm, to take care of wall orthogonality and skewness correction.

Please provide some validated 2-D flux calculating algorithm for high-speed flows in any programing language.
Thank you.

Transfinite interpolation will only get you so far. There are smoothing algorithms that try to relax away the skewness/non-orthogonality, both at the walls and in the bulk. If you need smooth meshes, you should probably look into PDE-based grid generation.

https://perso.uclouvain.be/vincent.l...jfr-cours4.pdf

Thank you sir
Is there any algorithm exist to make algebraic grids orthogonal at least in boundaries of blocks.
Please tell me switching to PDE based mesh generator is the only way to make orthogonal?

There are many grid smoothing algorithms.

http://www.imr.sandia.gov/papers/topics/smooth.html
http://graphics.stanford.edu/courses..._smoothing.pdf

Laplacian Smoothing (basically...local mesh averaging) is a simple option. There are sping and spring/torsion models. There are variational approaches. I am no expert, but there are lots of fairly intuitive ways to smooth out meshes.

BTW, you *FORCE* the mesh at the walls and block boundaries to be orthogonal by forcibly moving the adjacent nodes to line up and then smooth the rest of the mesh into alignment while keeping those fixed. That will ensure that you have the boundary mesh that is perfectly orthogonal and an internal mesh that is relaxing towards orthogonality.

Elliptic grid generation does a similar thing, as you solve the PDE system using a relaxation algorithm. On a fundamental level, the calculations and results will likely be similar even if the formulations are very different.

So for I used such kind of things like smoothing and wall orthogonality stuffs only commercial packages like ICEM-CFD and pointwise. In those Softwares, basic block mesh would look similar to an algebraic grid. After that, we can use wall orhogonality correcting algorithm, different smoothing algorithm. Sometimes that ends up in a highly skewed mesh but I didn't know the algorithm behind it. Basic algorithm looks relatively simple but I personally feel that is computationally expensive for big grid generation. They affect skewness by orthogonality correcting algorithm and orthogonality by smoothing algorithm. Thank you, sir.

Orthogonality at the block level is the core of what GridPro does. Check the works of Peter Eiseman and his colleagues. Many of them are AIAA conference papers.

Just to clarify, you are not formally solving a pde per se, but you have a problem that looks like a pde. It is similar to how you can apply Newton's laws to a fluid element and from there come up with the Navier-Stokes equations (a pde).

You have a grid and you like to force it to obey some constraints which is like smoothing under some metric: uniformness, orthogonality, skewness, etc. In order to force your grid to satisfy these constraints, you apply a force to it and these metrics will respond. You want to do this for all cells. Hence you write it as a big coefficient matrix, which can be interpreted as the linearized form of some pde. Once you recognize the connection between gridding and solving a pde, it allows you to come up with some mathematical formalisms makes a general purpose gridder easier to analyze and implement. But solving this smoothing problem is not necessarily as difficult as a pde, it is more likely to be an algebraic problem.