新的求解二维浅水方程的高分辨率有限体积法

A New High-resolution Finite Volume Method for Solving Shallow Water Equations

随着海洋开发、灾害预防等方面的发展,浅水方程的求解越来越受到人们的重视。文中在文献[1]的基础上提出一种新的求解二维浅水方程的有限体积格式,并将文献[2]中给出的新型可微限制器函数运用到上述有限体积法求解二维浅水波问题的过程当中,建立新的可求解二维浅水方程的新的高分辨率有限体积法。文中提出的方法由预估阶段和校正阶段组成,该方法是在非结构化三角网格中实现的。运用这种方法模拟超临界流斜水跃现象,数值试验结果显示所提出的有限体积法具有很好的非震荡性。

With the development of ocean development,disaster prevention and other aspects, solving shallow water equation is paid more attention. In this paper,made an improvement for a new finite volume method （FVM） in the numerical solution of shallow water equa- tions based on document [ 1 ] ,and applyed the new limter in document [2] to above FVM to solve the shallow water problem,present a new high-resolution finite volume method. The proposed approach consists of a predicting stage and a correcting stage. The proposed method is implemented on unstructured meshes. It combines the new FVM to simulate supercritical flow oblique hydraulic jump problem, numerical results show that the proposed finite volume method is well non-oscillatory.