基于变分原理的自适应网格技术及其权函数问题研究

利用两个具有解析解的算例研究基于变分原理的自适应网格技术。结果表明,对运动激波算例,权函数考虑二阶导数项比考虑梯度项更能有效地减小误差;对气旋锋生算例,仅以梯度作为权函数亦不能提高精度,考虑速度场、锋生函数分布的权函数能更合理地安排网格;对照解析解,发现提出的自适应网格技术能明显提高计算精度,在节省内存等方面显示了突出的优点。

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.