Repository: Freie Universit├Ąt Berlin, Math Department

A Semi-Implicit Multiscale Scheme for Shallow Water Flows at Low Froude Number

Vater, S. and Klein, R. (2018) A Semi-Implicit Multiscale Scheme for Shallow Water Flows at Low Froude Number. Communications in Applied Mathematics & Computational Science, 13 (2). pp. 303-336. ISSN 1559-3940


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A new large time step semi-implicit multiscale method is presented for the solution of low Froude-number shallow water flows. While on small scales which are under-resolved in time the impact of source terms on the divergence of the flow is essentially balanced, on large resolved scales the scheme propagates free gravity waves with minimized diffusion. The scheme features a scale decomposition based on multigrid ideas. Two different time integrators are blended at each scale depending on the scale-dependent Courant number for gravity wave propagation. The finite-volume discretization is based on a Cartesian grid and is second order accurate. The basic properties of the method are validated by numerical tests. This development is a further step in the development of asymptotically adaptive numerical methods for the computation of large scale atmospheric flows.

Item Type:Article
Additional Information:SFB 1114 Preprint: 12/2017
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > Geophysical Fluid Dynamics Group
ID Code:2141
Deposited By: Silvia Hoemke
Deposited On:04 Dec 2017 15:02
Last Modified:19 Mar 2019 15:10

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