求解温盐双扩散系统的一种高精度方法

A high order method for thermohaline driven flow system

引入边界拟合坐标系来研究温盐双扩散系统。为了提高求解的精确性 ,对流项采用四阶精度的迎风格式 ,扩散项和涡量方程的浮力项则采用四阶精度的中心差 ,因此本文的方法是高精度的方法。首先针对温度占优( Rρ=0 .32 )和盐度占优 ( Rρ=1 .6 8)的情形进行了验证性计算 ,得到了与前人一致的结果。进一步 ,本文系统给出了不同的盐度通量强度下的流动形态 ,包括对称结构 ,不对称结构 ,反转结构等 ,结果与前人的吻合。

In this paper, incompressible, thermohaline double diffusive convection system is simulated using finite difference schemes with the boundary fitted coordinate system. The finite difference methods used include the high order accurate upwind difference scheme. The proposed method is first applied to the symmetric states of a salinity dominated flow with R ρ=1.68 and a temperature dominated flow with R ρ=0.32. Then the method is applied to symmetry breaking and overturning states in thermohaline driven flows in two dimensional rectangular and trapezoid basins. The numerical results agree well with those by Quon & Ghil and Dijkstra & Molemaker.