A Method for Orthogonal Grid Generation

A grid is called orthogonal if all grid lines intersect at a right angle. An or thogonal grid o ers signi cant advantages in the solution of systems of partial differential equations and in the simulations of computational uid dynamics. In this paper we present a variational method which generates nearly orthogonal grids with suitable parameter values. We optimize a cost functional which consists of only area and orthogonality quantities. A signi cant contribution is that no volume functional needs to be added to the cost functional. We achieve to generate nearly orthogonal grids without changing the cell size distribution of the initial grids by well-achieved deformation based grid generation method.