摘要
σ坐标变换应用于海洋流动数学模型,近年来得到了广泛的应用。坐标变换对于自由表面的捕捉及床面的描述具有很好的适用性,但变换后动量方程中的扩散项形式较复杂,数值求解难度加大。目前在数值求解中通常采用适当的简化,计算得到简化的同时带来了新问题。目前的简化方式带来了计算的精度问题,针对纯扩散问题,将产生附加运动,如对于盐度、泥沙等的扩散运动,将会产生附加的输运量,偏离物理本质。本文结合部分学者的研究工作,着重分析了误差产生的问题所在,进而提出一种改进的数值计算方法。通过算例验证,表明文中所给计算方法对于原有处理方法有相当程度上的改进,可应用于该类模型的数值求解。
When the σ coordinates is used in mathematical models of hydrodynamic flows in seas and estuaries, a significant numerical error will be generated in the case of strong changes of topography. An artifical flow or additional transport process of salinity and sediment appears due to the numerical error in computation. An approach of solving the horizontal diffusion term in original coordinates (x, z) was pro posed in which the variables in original coordinates ( x, z) were interpolated from those defined in σ coordinate. The finite difference method was used to solve one dimensional diffusion equation to validate the approach. It shows that the proposed approach is of high accuracy and efficiency.
出处
《力学季刊》
CSCD
北大核心
2006年第3期377-386,共10页
Chinese Quarterly of Mechanics
关键词
σ坐标系
水平扩散
σ coordinate
horizontal diffusion