Temporal Discretization Algorithms for the Continuity Equation of the One-dimensional Shallow Water Model

抄録

  Cross-sectionally averaged one-dimensional shallow water equations (1-D SWEs) serve as a fundamental tool in simulating open channel flows. Accurate numerical simulation of transient flows is crucial for practical analysis of mass and momentum transport phenomena in open channels. Temporal discretization algorithm is the one of the most influential factors that controls accuracy, stability and computational efficiency of numerical simulation. This paper presents a new numerical method for the 1-D SWEs, referred to as SElective LUmping Method (SELUM), which is an intermediate method between the Finite Element/Volume Method (FEVM) and Dual Finite Volume Method (DFVM) previously developed by the authors. The SELUM selectively lumps the mass matrix of the continuity equation so that stable numerical solutions are obtained even under severe flow conditions where the FEVM or DFVM fail. An approximate mass matrix inversion method is incorporated into the SELUM to improve computational efficiency while not to degrade accuracy and stability. Numerical simulations of idealized and experimental problems are carried out to demonstrate its advantages over the existing numerical methods.