An explicit finite difference model for simulating weakly nonlinear and weakly dispersive waves over slowly varying water depth

作者：Wang Xiaoming; Liu Philip L F^*

来源：Coastal Engineering, 2011, 58(2): 173-183.

DOI：10.1016/j.coastaleng.2010.09.008

• Tsunami
• Numerical modeling
• Shallow water waves
• Frequency dispersion
• Numerical dispersion
• Boussinesq equations

In this paper, a modified leap-frog finite difference (FD) scheme is developed to solve Non linear Shallow Water Equations (NSWE). By adjusting the FD mesh system and modifying the leap-frog algorithm, numerical dispersion is manipulated to mimic physical frequency dispersion for water wave propagation. The resulting numerical scheme is suitable for weakly nonlinear and weakly dispersive waves propagating over a slowly varying water depth. Numerical studies demonstrate that the results of the new numerical scheme agree well with those obtained by directly solving Boussinesq-type models for both long distance propagation, shoaling and re-fraction over a slowly varying bathymetry. Most importantly, the new algorithm is much more computationally efficient than existing Boussinesq-type models, making it an excellent alternative tool for simulating tsunami waves when the frequency dispersion needs to be considered.

• 出版日期2011-2
• 单位中央民族大学