σ坐标系下浅水方程水平扩散项守恒型式

Conservative model of horizontal diffusion term of shallow water equations in σ coordinate

三维浅水模型控制方程经σ坐标变换后,其水平扩散项还存在一变换因子,故不能被常见的扩散模型表示成守恒型式。对σ坐标系下浅水方程水平扩散项进行处理,得到守恒型式的扩散模型,并采用垂向二维静水盐度扩散算例进行验证,结果表明守恒型模型能够保持初始的盐度分布。

For shallow water equations in σ coordinate,the horizontal diffusion term has an factor,which leads to non-conservative form exploiting now diffusion models.The paper deals with the diffusion term and deduces a conservative diffusion model,which is tested by the classical example of salinity diffusion in still water.The result shows that the conservative diffusion model is capable of preserving the initial salinity status.