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σ-坐标是地表水三维水动力及物质输运模型使用最多的垂向坐标,但陡坡区域水平压力梯度误差长期制约着σ-坐标在海洋模拟中的发展,现有解决方法如z-平面法、相对密度法、提高精度法和地形光滑法等都未取得满意的结果.本文提出σ-数值切割单元法,在陡坡区域引入伪床面,降低H/x,消除了长期存在的区域水平压力梯度问题,将问题转化为陡坡位置的非贴体网格问题,进一步采用数值切割单元法解决边界拟合问题.对数值切割单元法的关键步骤,如床面数值识别、网格单元或节点分类、数值源项的半隐式求解以及切割速度的插值计算,提出适合于地表水地形分布特性的具体解决方法.模型既利用了传统σ-网格的简单高效性,又克服了σ-坐标在陡坡或复杂地形中应用的局限性,实现了σ-坐标和数值切割单元法的联合优势.理想海山试验表明,σ-数值切割单元法所产生的最大速度误差相对z-平面法减小近一倍,全域动能误差减小两个量级左右.海沟、海山、大陆架及河口区域存在下的复杂地形数值试验表明,模型对复合陡坡地形同样具有很好的适应性.
The σ-coordinate is the most widely used vertical coordinate for the three-dimensional hydrodynamic and material transport models of surface water. However, the horizontal pressure gradient error in the steep slope has restricted the development of σ-coordinates in marine simulation for a long time. Existing solutions such as z-plane method , The relative density method, the accuracy improvement method and the terrain smoothing method have not obtained the satisfactory results.In this paper, the σ-numerical cutting unit method is introduced in the steep slope region to introduce a pseudo-bed, reducing H / x, eliminating the long-standing region Horizontal pressure gradient problem, the problem is transformed into the non-skinned grid problem of steep slope location, and the numerical boundary element problem is further solved by using the numerical cutting element method.The critical steps of the numerical cutting element method, such as bed numerical identification, Node classification, semi-implicit solution of numerical source term and interpolation of cutting speed, a specific solution to the distribution characteristics of surface water topography is proposed.The model not only takes advantage of the simple and efficient traditional σ-grid but also overcomes the problem of σ- The limitations of the application of coordinates in steep slopes or complex terrains have realized the combined advantage of the σ-coordinate and numerical cutting unit method.The ideal seamount tests show that the σ- Compared with the z-plane method, the error of maximum speed of birth decreases nearly two times and the global kinetic energy error decreases about two orders of magnitude.The numerical experiments of complex topography in the presence of trenches, seamounts, continental shelves and estuaries show that the model is similar to the compound steep terrain Has a good adaptability.