Nonlinear wave modeling in very shallow water

Document Type

Conference Proceeding

Date of Original Version



An existing model based on fully nonlinear potential flow equations is used to study wave propagation. The solution approach combines a higher-order Boundary Element Method (BEM) for solving Laplace's equation at a given time, and Lagrangian Taylor expansions for the time updating of the free surface position and potential. Shoaling and breaking of solitary waves are calculated in very shallow water, which requires solving the problem in computational domains with sharp geometry and large aspect ratios. Accuracy of the solution is improved by using a new interpolation technique (first introduced in 11), and accurate quasi-singular integration techniques based on modified Telles and Lutz methods. Applications are presented that demonstrate the accuracy and efficiency of the new approaches.

Publication Title

Boundary Elements XV: Fluid Flow and Computational Aspects