四阶紧致差分格式对静力模式中垂直网格计算频散性的影响

为了说明四阶紧致差分格式在大气和海洋数值模式中的潜在价值,提出一种通用方法,推导静力线性斜压适应方程组在微分和差分情况下的频散关系,水平尺度分100 km,10 km和1 km三种情况,从频率、水平群速和垂直群速方面,对采用二阶中央差和四阶紧致差分格式情况下,非跳点网格(N网格)、Lorenz网格(L网格)、Charney-Phillips网格(CP网格)、Lorenz时间跳点网格(LTS网格)和Charney-Phillips时间跳点网格(CPTS网格)的计算特性进行比较,发现采用高精度的四阶紧致差分格式总体上可以明显减少上述三种水平尺度波动在N网格、CP网格、L网格和CPTS网格上的频率、水平群速和垂直群速误差,但对LTS网格,采用四阶紧致差分格式,会使得计算水平群速和垂直群速误差变大.

Difference Schemes on Vertical Grids in a Hydrostatic Model

To study forth-order compact schemes in numerical atmospheric or oceanic models,a general method is proposed for dispersion relation of hydrostatic linear baroclinic adjustment equations with differential or difference schemes,at horizontal length of 100 km,10 km and 1 km,respectively.Non-staggered grids(N grids),Lorenz grids(L grids),Charney-Phillips grids(CP grids),Lorenz time staggered grids(LTS grids) and Charney-Phillips time staggered grids(CPTS grids) in a second-order centered scheme and a forth-order compact scheme are compared.The forth-order compact scheme reduces errors of frequency,horizontal and vertical component of group velocity on N grids,CP grids and CPTS grids obviously,but increases errors of horizontal and vertical component of group velocity on LTS grids.