Modelling coastal water waves using a depth-integrated, non-hydrostatic model with shock-capturing ability

ABSTRACT

This paper presents a depth-integrated, non-hydrostatic model for coastal water waves. The shock-capturing ability of this model is its most attractive aspect and is essential for computation of energetic breaking waves and wet–dry fronts. The model is solved in a fraction step manner, where the total pressure is decomposed into hydrostatic and non-hydrostatic parts. The hydrostatic pressure component is integrated explicitly in the framework of the finite volume method, whereas most of the existing models use the finite difference method. The fluxes across the cell faces are computed in a Godunov-based manner through an efficient multi-stage scheme. The flow variables are reconstructed at each cell face to obtain second-order spatial accuracy. Wave breaking is treated as a shock by locally switching off the non-hydrostatic pressure in the wave front. A moving shoreline boundary is also incorporated. The robustness and accuracy of the developed model are demonstrated through numerical tests.

Keywords:

• Finite volume method
• MUSTA scheme
• non-hydrostatic model
• shock-capturing
• wave breaking

Acknowledgements

The authors are grateful to three anonymous reviewers for their careful reviews and many useful suggestions. The valuable suggestions from Professor Ping Dong from University of Dundee are also acknowledged.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 51009018]; National Marine Environment Monitoring Center [grant number 210206]; Key Laboratory of Water-Sediment Sciences and Water Disaster Prevention of Hunan Province [grant numbers 2013SS02 and 2012SS02].