Solution-adaptive techniques in computational heat transfer and fluid flow

Recent contributions to solution-adaptive grid and solution-adaptive differencing techniques are breifly described in this paper. In solution-adaptive grid techniques, the grid points are dynamically reclustered or refined to improve the resolution in the important regions where the truncation error estimate is high. In solution-adaptive differencing techniques, the order of the differencing scheme in high error estimate region is dynamically increased. Thus both adaptive grid and adaptive differencing techniques represent error-equidistribution procedures. Two strategies for adaptive gridding are described in this paper. In one strategy, termed Global Adaptation, all grid points participate in the grid point redistribution process. In the other strategy, called Local Adaptation, grid refinement is performed only in local regions with high truncation error estimates. Results of various problems are presented which show the improvements obtained with solution-adaptive techniques.