Shallow moment models are extensions of the hyperbolic shallow water equations.They admit variations in the vertical profile of the horizontal velocity.This paper introduces a non-hydrostatic pressure to this framework and shows the systematic derivation of dimen-sionally reduced dispersive equation systems which still hold information on the vertical profiles of the flow variables.The derivation from a set of balance laws is based on a split-ting of the pressure followed by a same-degree polynomial expansion of the velocity and pressure fields in a vertical direction.Dimensional reduction is done via Galerkin projec-tions with weak enforcement of the boundary conditions at the bottom and at the free sur-face.The resulting equation systems of order zero and one are presented in linear and non-linear forms for Legendre basis functions and an analysis of dispersive properties is given.A numerical experiment shows convergence towards the resolved reference model in the linear stationary case and demonstrates the reconstruction of vertical profiles.
Shallow flowFree surface flowNon-hydrostatic modelDispersive equationsMoment approximationHyperbolic systems
Ullika Scholz、Julia Kowalski、Manuel Torrilhon
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Applied and Computational Mathematics(ACoM),RWTH Aachen University,Aachen,Germany
Methods for Model-based Development in Computational Engineering(MBD),RWTH Aachen University,Aachen,Germany
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