A new efficient method of generating solution-adaptive grids for cascade problems is introduced. General Poisson-type grid generation systems are used to generate the adaptive grid from an initial grid. This scheme uses Laplace equations, which are then transformed by using stretching functions to the final computational domain so that the generated grid can be clustered in the desired regions. Thus, the resulting generating equations are linear and uncoupled. To adapt the grid to solutions, the control functions are chosen to depend upon the curvature and the gradient of the solution at each grid point and the grid spacing is controlled by these values.
This scheme is tested on various model problems in one and two dimension. Lastly, this adaptive grid equations are employed for transonic flow calculations. The adaptive grid solution, which is compared with the fixed grid solution, shows a better solution which shows a sharp discontinuity across shock. Therefore, the adaptive grid generation system presented in this study is very efficient relative to other generation systems.
