二维浅水流动的一种普适的高性能格式——有限体积Osher格式

天然水体具有形状复杂的计算区域和水下地形。本文采用无结构的网格以适合这一情况,并能方便地根据工程应用的要求局部地和适应性地加密网格。相应地,对二维水流计算问题采用了有限体积法的数学表示。跨单元边界的法向数值通量通过用Osher格式求解黎曼问题得到。文中给出了适合于二维浅水方程组的有关单元界面和各种物理边界的法向数值通量公式。分析了这一格式所具有的优点,包括:普适性、守恒性、逆风性、单调保持性、高效性、对间断的高分辨率、边界处理和内部格式相容,以及不引入数值边界条件等。最后,通过长江口南支水流计算的实例,阐明其良好性能。

A Universal High-Performance Algorithm for Two-Dimensional Unsteady Shallow Water Flow Computation——The Finite-Volume Osher Scheme

The unstructured mesh is adopted, which can be refined locally and adaptively according to the planar geometry of computational domain, bathymetry, and the requirements of specific engineering applications. The two-dimensional open flow computation problem is formulated with the finite volume method. Numerical flux in the normal direction to and across each side of elements is obtained by solving a Riemann problem by using Osher's scheme. Related formulas of normal numerical flux are derived. The merits of the new algorithm are pointed out, including: universality, conservativity, upwindness, high efficiency, monotonicy-preserving, high resolution in discontinuities, consistency between boundary procedure and internal scheme, nonexistence of numerical boundary conditions, etc. Lastly, the good performance is demonstrated through a case study of tidal flow computation for the southern branch of the Yangtze estuary.