Absorbing–generating seaward boundary conditions for fully-coupled hydro-morphodynamical solvers

Incelli, Giorgio; Briganti, Riccardo; Dodd, Nicholas

Abstract

This paper presents a new technique to compute open boundary conditions for fully-coupled hydro-morphodynamical numerical solvers based on the Non-Linear Shallow Water and the Exner equations. These conditions allow the generation of incident signals and the absorption of reflected ones, taking into account the bed evolution at the boundary. They use the approximations for linear waves in shallow water and are based on the solution of the Riemann Equations.

The proposed technique is implemented in the fully-coupled hydro-morphodynamical numerical model of Briganti et al. (2012a).

Firstly, the generation and absorption of single monochromatic waves are studied to quantify the error after the reflected wave exited the domain. In all cases the error is always small, giving evidence of the effectiveness of the new seaward boundary conditions.

Furthermore, the propagation and reflection of a monochromatic wave train over a mobile bed are considered. Both flow evolution and bed change are not affected by spurious oscillations when long sequences of waves are tested. Additionally, a very low mobility bed is considered to simulate a ‘virtually fixed’ bed and new boundary condition results consistently converge to those for the hydrodynamic only case.

Finally, the reflection of a uniform bore over a mobile bed is studied. For this case the Rankine–Hugoniot conditions provide an analytical solution. It is apparent that the adopted linear approximations produce errors in the velocity estimates. Nevertheless, the conditions perform reasonably well even in this demanding non-linear case.

Citation

Incelli, G., Briganti, R., & Dodd, N. (2015). Absorbing–generating seaward boundary conditions for fully-coupled hydro-morphodynamical solvers. Coastal Engineering, 99, https://doi.org/10.1016/j.coastaleng.2015.02.002

• Journal Article Type: Article
• Acceptance Date: Feb 3, 2015
• Online Publication Date: Feb 23, 2015
• Publication Date: May 31, 2015
• Deposit Date: Aug 4, 2017
• Publicly Available Date: Aug 4, 2017
• Journal: Coastal Engineering
• Print ISSN: 0378-3839
• Electronic ISSN: 0378-3839
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 99
• DOI: https://doi.org/10.1016/j.coastaleng.2015.02.002
• Keywords: Fully-coupled morphodynamics, Open boundary, Absorbing-generating boundary conditions, Non-Linear Shallow Water Equations, Exner equation
• Public URL: https://nottingham-repository.worktribe.com/output/750954
• Publisher URL: http://www.sciencedirect.com/science/article/pii/S0378383915000253?via%3Dihub
• Contract Date: Aug 4, 2017