What is the general concenous on the aplication of wall functions within turb models? i.e. the use of adaptive grid, coles Law, shape function, etc.

Although I will not directly answer your questions (because I don't know the answers) but i may direct you to where you might get them. In an adaptive grid, the physics of the problem at hand must ultimately direct the grid points to distribute themselves so that a functional relationship on these points can represent the physical solution with sufficient accuracy. The idea is to have the grid points move as the physical solution develops, concentrating in regions of large variation in the solution as they emerge. The mathematics controls the points by sensing the gradients in the evolving physical solution, evaluating the accuracy of the discrete representation of the solution, communicating the needs of the physics to the points, and finally by providing mutual communication among the points as they respond to the physics. The basic techniques involved then are as follows:

(1) a means of distributing points over the field in an orderly fashion, so that neighbors may be easily identified and data can be stored and handled efficiently.

(2) a means of communication between points so that a smooth distribution is maintained as points shift their position.

(3) a means of representing continuous functions by discrete values on a collection of points with sufficient accuracy, and a means for evaluation of the error in this representation.

(4) a means for communicating the need for a redistribution of points in the light of the error evaluation, and a means of controlling this redistribution.

for further information on the grid problem you can contact the good text (availabe online) about the numerical grid generation: http://www.erc.msstate.edu/publications/gridbook/ The whole chapter XI in this book is about adaptive grids so you might get the answer there. About the shape functions you can contact of the good reference of the finite elements, the shape function is heavily discussed.