四阶紧致差分格式对三维网格计算特性的影响

为了研究四阶紧致差分格式对三维网格计算特性的影响,引进了一种推导斜压地转适应过程频散关系的通用方法,采用二阶中央差和四阶紧致差分格式从频率和群速度两个方面比较在各种三维网格上描述斜压地转适应过程产生误差的情况.结果表明,采用高精度的四阶紧致差分格式仅能提高三维网格C/LTS和EL/LTS的计算特性,而对其他几种三维网格的影响则不是正面的.四阶紧致差分格式在大气或海洋数值模式中应慎用.

Impact of fourth -order compact difference scheme on computational properties of 3D grids

To inv estiga te the impact of a fourth-o rder compact di fference scheme o n computa tio nal properties o f 3D g rids, a unified metho d w as int roduced to deriv e the di spersion rela tionship of baroclinic g eo stro phic adjustment pro cess. Using the seco nd-order cent ral di fference scheme and the fo ur th-order compact dif ference scheme, the errors produced o n 3D g rids in describing baroclinic g eostro phic adjustment process relativ e to the dif ferential case were intui tio nally compared w ith each o ther f rom the aspect s o f f requency a nd g roup v eloci ty respectiv ely. Th e resul t show s that by using four th-order compact dif ference scheme wi th higher precisio n the computational pro perties o f three dimension C /LTS g rid and EL /LTS g rid can be improved, w hi le the impact on o ther g rids i s no t po sitiv e. So the fo ur th-order compact di fference scheme should be carefully used wi thin the co ntex t o f numerical atmospheric o r ocea nic models