Hyperbolic Solution Adaptive Mesh Generation

In recent years there has been much activity in the development of solution adaptive mesh procedures as one method of increasing the efficiency and accuracy of numerical solutions of the Euler and Navier-Stokes equations. Most of the adaptive mesh procedures are based on a set of elliptic equations describing the location of the grid points subject to certain smoothness and orthogonality constraints. The computational effort to solve these equations is of the same order as that required to solve the flow equations. This additional cost of generating the adapted mesh negates much of the advantage of adapted meshes, i.e. computational efficiency. An alternative method of generating a solution adapted mesh is presented. The method is based on the hyperbolic grid generation procedure of [1] and is much faster than those based on elliptic grid generators.