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You are here : eLibrary : IAHR World Congress Proceedings : 36th Congress - The Hague (2015) ALL CONTENT : Water engineering : Adaptive, multiresolution, discontinuous galerkin shallow water modelling
Adaptive, multiresolution, discontinuous galerkin shallow water modelling
Author : CAVIEDES-VOULLIÈME, D.(1), KESSERWANI, G.(1) ,GERHARD, N.(2) & MÜLLER, S.(2)
ABSTRACT
Shallow water modelling poses challenges not only on the formulation of numerical schemes, but also in modelling and
solving the different spatial and temporal scales involved. Many applications of shallow water modelling including flood
simulation and coastal simulation often require representing and solving very large domains, while being able to include
small scale topography features and track moving and transient flow features, such as shocks and wet/dry fronts.
Adaptive meshes can provide the optimal solution for the multiresolution problem that shallow water problems pose, and
indeed a number of strategies have been implemented and tested. However, in most cases, adaptivity is governed by
extrinsic, user-controlled criteria which are not necessarily optimal from neither the accuracy nor efficiency point of
views. This work presents an adaptive, multiresolution Shallow Water solver, based on the Discontinuous Galerkin
method and multiwavelets (MWDG). The mathematical properties of the MWDG scheme allow for it to automatically
adapt over a large number of resolution levels using information from the solution itself and a single user-specified
parameter. This is done via the filter action that multiwavelets can exert on the DG modal decomposition of the partial
differential equations. We present the fundamentals of the SW-MWDG formulation, show that desirable properties for
Shallow Water modelling are enforced and guaranteed under adaptive meshes (well balancing and positivity preserving)
and include benchmarking cases.
File Size : 2,148,169 bytes
File Type : Adobe Acrobat Document
Chapter : IAHR World Congress Proceedings
Category : 36th Congress - The Hague (2015) ALL CONTENT
Article : Water engineering
Date Published : 19/08/2015
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