Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5500480 | Wave Motion | 2017 | 56 Pages |
Abstract
An accurate and fast numerical method is developed to investigate the nonlinear (linear) shallow water wave propagation over flat (depth-varying) topography in one space dimension within an irrotational and inviscid flow. As physical model, we use a dispersive Boussinesq-type (BT) system for small-amplitude long waves with weak transverse variation. The problem is discretised in space using a wavelet-Galerkin method based on one-periodic Daubechies scaling functions. Assuming periodic boundary conditions, the discretised operators in spatial domain are circulant and skew-symmetric. These characteristics of discretised differential operators allow us to incorporate the Fast Fourier Transformation (FFT) in the matrix operations which results in a substantial improvement in the computational efficiency and accuracy of the numerical solver compared with the conventional finite difference or finite volume methods. We use a four-stage Runge-Kutta method to temporally discretise the governed spatially discretised differential equations. Several comparative test cases are conducted to validate the performance and efficiency of the proposed wavelet-Galerkin scheme for the BT model over flat beds relative to some existing analytical solutions and numerical results from a second-order finite difference method. We examine the numerical results of the BT system to investigate the two-way propagation of waves for some large L2-norm profiles of the initial free-surface elevation. We also assess the ability of the proposed method to predict the evolution and breaking of undular bores over a flat bed with a simple kinematic criterion. Moreover, we study (tsunami) wave runup and propagation by incorporating the effects of depth-varying topography in a simplified BT system in order to check the applicability of the approach to capture the interactions between the bathymetric features and the wet cells.
Keywords
Related Topics
Physical Sciences and Engineering
Earth and Planetary Sciences
Geology
Authors
M. Bakhoday-Paskyabi,