Although G-coordinate is one of the most popular methods used in marine and estuarine modeling, it has long suffered from the so-called ＂steep boundary problem＂, namely, the PGF problem. In this paper, a new method called the ＂σ-sharpen immersed boundary method＂ （σ-SIBM） is put forward. In this method, the virtual flat bottom boundary is creatively introduced in regions with the steep boundary and is taken as the boundary of numerical domain. By this, OH/Ox of numerical domain changes to be a controllable value and the steep bottom problem is then transformed to the non-conforming boundary problem, which is, in turn, solved by the SIBM. The accuracy and efficiency of the σ-sharpen immersed boundary method （σ-SIBM） has been showed by both comparative theoretical analysis and classical numerical tests. First, it is shown that the σ-SIBM is more effective than the z-level method, in that σ-SIBM needs special treatment only in the steep section, but the z-level method needs the special treatment in each grid note. Second, it is superior to the p-method in that it is not restricted by the density distribution. This paper revisits the classical seamount numerical test used in numerous studies to prove the sigma errors of the pressure gradient force （PGFE） and their long-term effects on circulation. It can be seen that, as for the maximum erroneous velocity and kinetic energy, the value of σ-SIBM is much less than that of the z-level method and the traditional σ-method.
赣江下游受江湖关系顶托影响,水流运动极为复杂,水位流量关系年际变化显著。通过建立正交曲线坐标系平面二维浅水方程ELADI(Eulerian-Lagrangian alternating direction implicit method)有限差分方法的水动力模型对赣江河流下游进行了水位,流速与东西河分流比验证和连续十年的分流比模拟,分析了水位流量关系和分流比的变化特征。模拟与分析结果表明,模型高效稳定,计算结果与实测资料吻合良好,可用于河流水动力的数值模拟与预测。
