Numerical techniques for the transformation to an orthogonal coordinate system aligned with a vector field

We explore the use of variational grid-generation to perform alignment of a grid with a given vector field. Variational methods have proven to be a powerful class of grid-generators, but when they are used in alignment, difficulties may arise in treating boundaries due to an incompatibility between geometry and vector field. In this paper, a refinement of the procedure of iterating boundary values is presented. It allows one to control the quality of the grid in the face of the above-mentioned incompatibility. This procedure may be incorporated into any variational alignment algorithm. We demonstrate its use with respect to a new quasi-variational alignment method having a particularly simple structure. The latter method is comparable to Knuppʹs method (see [1]), but avoids use of the Winslow equations.