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Implementation of ADER scheme for a bore on an unsaturated permeable slope
Author(s) -
Steenhauer K.,
Pokrajac D.,
O'Donoghue T.
Publication year - 2011
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.2706
Subject(s) - finite volume method , infiltration (hvac) , nonlinear system , mechanics , quadratic equation , geotechnical engineering , ode , mathematics , geology , geometry , physics , meteorology , quantum mechanics
SUMMARY The paper details the implementation of the Godunov‐type finite volume Arbitrary high order schemes using Derivatives (ADER) scheme for the case of a large source term in the continuity equation of the nonlinear shallow water equations. The particular application is the movement of a bore on a highly permeable slope. The large source term is caused by the infiltration into the initially unsaturated slope material. Infiltration is modelled as vertical downwards piston‐like flow with Forchheimer quadratic parameterisation of the resistance law. The corresponding ODE is solved using the fourth‐order Runge–Kutta method. The surface and subsurface flow models have been tested by comparison with analytical solutions. Example predictions of surface bore propagation and wetting front propagation are presented for a range of slope permeabilities. The effects of permeability on bore run‐up, water depths and velocities are illustrated. The ADER scheme is capable of handling the source term, including the extreme case when this term dominates the volume balance. Copyright © 2011 John Wiley & Sons, Ltd.