JAMP  Vol.2 No.6 , May 2014
A Well-Balanced Numerical Model for the Simulation of Long Waves over Complex Domains
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.
Cite this paper: Wu, G. , He, Z. , Liu, G. (2014) A Well-Balanced Numerical Model for the Simulation of Long Waves over Complex Domains. Journal of Applied Mathematics and Physics, 2, 418-424. doi: 10.4236/jamp.2014.26050.

[1]   Dodd, N. (1998) Numerical Model of Wave Run-Up, Overtopping, and Regeneration. ASCE Journal of Waterway, Port, Coastal and Ocean Engineering, 124, 73-81.

[2]   Hu, K., Mingham, C.G. and Causon, D.M. (2000) Numerical Simulation of Wave Overtopping of Coastal Structures Using the Non-linear Shallow Water Equations. Coastal Engineering, 41, 433-465.

[3]   Hubbard, M.E. and Dodd, N. (2002) A 2D Numerical Model of Wave Run-up and Overtopping. Coastal Engineering, 47, 1-26.

[4]   Delis, A.I., Kazolea, M. and Kampanis, N.A. (2008) A Robust High-Resolution Finite Volume Scheme for the Simulation of Long Waves over Complex Domains. International Journal for Numerical Methods in Fluids, 56, 419-452.

[5]   Liang, Q., Wang, Y. and Archetti, R. (2010) A Well-Balanced Shallow Flow Solver for Coastal Simulations. International Journal of Offshore and Polar Engineering, 20, 41-47.

[6]   Bryson, S., Epshteyn, A., Kurganov, A. and Petrova, G. (2010) Well-Balanced Positivity Preserving Central-upwind Scheme on Triangular Grids for the Saint-Venant System. ESAIM: Mathematical Modelling and Numerical Analysis, 45, 423-446.

[7]   Liang, Q. (2010) Flood Simulation Using a Well-Balanced Shallow Flow Model. ASCE, Journal of Hydraulic Engineering, 136, 669-675.

[8]   Kurganov, A. and Petrova, G. (2007) A Second-Order Well-Balanced Positivity Preserving Scheme for the Saint-Ve-nant System. Communications in Mathematical Sciences, 5, 133-160.

[9]   Briggs, M., Synolakis, C., Harkins, G. and Green, D. (1995) Laboratory Experiments of Tsunami Runup on a Circular Island. Pure and Applied Geophysics, 144, 569-593.

[10]   Nikolos, I. and Delis, A. (2009) An Unstructured noDe-Centered ?nite Volume Scheme for Shallow Water Flows with Wet/Dry Fronts over Complex Topography. Computer Methods in Applied Mechanics and Engineering, 198, 3723- 3750.