Shallow-water sloshing in a moving vessel with variable cross-section and wetting-drying using an extension of George's well-balanced finite volume solver
Alemi Ardakani, H
Journal of Computational Physics
© 2016 Elsevier Inc. All rights reserved.
A class of augmented approximate Riemann solvers due to George (2008) is extended to solve the shallow-water equations in a moving vessel with variable bottom topography and variable cross-section with wetting and drying. A class of Roe-type upwind solvers for the system of balance laws is derived which respects the steady-state solutions. The numerical solutions of the new adapted augmented f-wave solvers are validated against the Roe-type solvers. The theory is extended to solve the shallow-water flows in moving vessels with arbitrary cross-section with influx-efflux boundary conditions motivated by the shallow-water sloshing in the ocean wave energy converter (WEC) proposed by Offshore Wave Energy Ltd. (OWEL). A fractional step approach is used to handle the time-dependent forcing functions. The numerical solutions are compared to an extended new Roe-type solver for the system of balance laws with a time-dependent source function. The shallow-water sloshing finite volume solver can be coupled to a Runge-Kutta integrator for the vessel motion.
The research reported in this paper is supported by the EPSRC under Grant number EP/K008188/1. Due to confidentiality agreements with research collaborators, supporting data can only be made available to bona fide researchers subject to a non-disclosure agreement. Details of the data and how to request access are available from the University of Surrey publications repository: firstname.lastname@example.org. The authors are grateful to both referees for their valuable comments.
This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.
Vol. 314, pp. 590 - 617