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. (English) Zbl 1349.76298
Summary: A class of augmented approximate Riemann solvers due to George (2008) [12] 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) [1]. 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.
MSC:
| 76M12 | Finite volume methods applied to problems in fluid mechanics |
| 65M08 | Finite volume methods for initial value and initial-boundary value problems involving PDEs |
Keywords:
shallow-water sloshing; hyperbolic conservation laws; finite-volume method; F-wave-propagation; wetting and drying; roe solverSoftware:
HLLEReferences:
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