Abstract
This paper presents a well-balanced two-dimensional (2D) finite volume model to simulate the propagation, runup and rundown of long wave. Non-staggered grid is adopted to discretize the governing equation and the intercell flux is computed using a central upwind scheme, which is a Riemann-problem-solver-free method for hyperbolic conservation laws. The nonnegative reconstruction method for water depth is implemented in the present model to treat the appearance of wet/dry fronts, and the friction term is solved by a semi-implicit scheme to ensure the stability of the model. The Euler method is applied to update flow variable to the new time level. The model is verified against two experimental cases and good agreements are observed between numerical results and observed data.
Highlights
Long waves, such as storm surges, tides, or tsunamis, will cause huge casualties and considerable property damage
The nonlinear shallow water (NLSW) equations are widely employed to model the physical process of long wave [1,2,3,4,5]
The models based on NLSW omit dispersive effects, these models are able to provide the general characteristics of the wave runup process [4]
Summary
Long waves, such as storm surges, tides, or tsunamis, will cause huge casualties and considerable property damage. It is important to develop an accurate and robust numerical model to predict and understand the propagation and runup of long wave. The nonlinear shallow water (NLSW) equations are widely employed to model the physical process of long wave [1,2,3,4,5]. A good long wave model should have two major properties, which are crucial for the stability of numerical model [6]: 1) The model should be able to be well balanced; 2) The model should preserve the water depth to be nonnegative. This paper presents a 2D well-balance shallow water model to simulate the propagation, runup and rundown of long wave. (2014) A Well-Balanced Numerical Model for the Simulation of Long Waves over Complex Domains.
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