Solution-adaptive grid procedure for high-speed parabolic flow solvers

A solution-adaptive grid procedure based on an error equidistribution scheme is developed and applied to a parabolized Navier-Stokes solver. An improved method of selecting weighting functions is introduced that involves normalizing a combination of flowfield gradients and curvature of a number of dependent variables and then selecting the largest at each point. The scheme redistributes grid points line by line with grid point motion controlled by forces analogous to tensional spring forces with the spring constants set equal to the weighting functions. Torsional terms are functions of the grid point positions along neighboring grid lines and provide grid smoothness and stability. A grid-fitting scheme is introduced for external flows in which the number of grid points in the freestream are reduced to a minimum.