Abstract: 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.