Adaptive Grid Technique Based on the Variational Principle and Its Weight Functions

Two computational cases that have analytic solutions are employed for studying the adaptive grid technique based on the variational principle. The results show that for the computational case of traveling shock waves the weight function, with the 2nd-order derivation terms taken into consideration, can more effectively reduce the error than one with gradient terms. For the case of cyclonic frontogenesis, weight functions only related to the gradient are unable to enhance the computational accuracy. while ones with the wind field and frontogenesis function taken into consideration can more reasonably arrange the grid. Compared with analytic solutions, the adaptive grid technique suggested in this paper can improve computational accuracy and it displays the prominent advantage of saving memory.