Local time stepping applied to mixed flow modelling

ABSTRACT

Mixed flows in closed conduits are characterized by waves, celerity values of which lie within a range of up to two orders of magnitude due to the simultaneous occurrence of free-surface and pressurized flow. If an explicit numerical scheme is used to simulate these phenomena, the time step necessary to guarantee stability is considerably restricted by pressure wave celerity, and thus the computational efficiency is reduced. In order to address this specific problem this paper proposes the application of the local time stepping strategy to a finite-volume scheme for mixed flow modelling, which adopts the Preissmann slot approach. The results of several tests show that local time stepping reduces run time significantly, compared to the conventional global time stepping, especially when only a small region of the domain is surcharged. The accuracy and mass conservation in the proposed approach are not impaired. Moreover, in the free-surface region of the flow the accuracy slightly improves.

Keywords:

• 1D shallow water equations
• finite volume
• local time stepping
• mixed flow
• numerical modelling
• Preissmann slot

Acknowledgements

We are grateful to the Associate Editor and the reviewers, whose valuable comments greatly contributed to improving the paper.