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.