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You are here : eLibrary : IAHR World Congress Proceedings : 36th Congress - The Hague (2015) ALL CONTENT : Water engineering : A comparison between different approaches for the numerical treatment of bottom discontinuities in a...
A comparison between different approaches for the numerical treatment of bottom discontinuities in a dg perspective
The use of Discontinuous Galerkin (DG) numerical schemes for the Shallow Water Equations (SWE) integration is greatly
increased in the last decade. The efforts of many researchers were initially devoted to conceive techniques for the exact
preservation of the motionless state over non-flat bottom. Recently, such efforts are mainly oriented to the proper
treatment of the bottom discontinuities and to the exact preservation of the moving-water steady flows.
In this work, in the unified context consisting of third-order accurate DG-SWE schemes, a comparison between five
numerical treatments of the bottom discontinuities is presented.
We consider three widespread approaches that perform well if the motionless state has to be preserved. First, a simple
technique, which consists in a proper initialization of the bed elevation that imposes the continuity of the bottom profile is
taken into account [Kesserwani and Liang, INT J NUMER METH ENG, 86, 47-69, 2011]. Then, we consider the
hydrostatic reconstruction method [Audusse et al., SIAM J SCI COMPUT, 25, 2050-2065, 2004] and a path-conservative
scheme based on a linear integration path [Parés, SIAM J NUMER ANAL, 44, 300-321, 2006].
We also consider two further approaches (both based on mechanical principles) which are promising for the preservation
of a moving-water steady state. A model is obtained modifying the hydrostatic reconstruction as suggested in [Caleffi and
Valiani, ASCE JEM, 135(7), 684-696, 2009]. This method is characterized by a correction of the numerical flux based on
the local conservation of the total energy. The last model is obtained improving the path-conservative scheme using a
non-linear path.
Several test cases are used to verify the accuracy, the well-balancing, the behavior in simulating a quiescent flow and the
resolution in simulating unsteady flows of the models. A specific test case is also introduced to highlight the difference
between the five schemes when a steady moving flow interacts with a bottom step.
File Size : 666,355 bytes
File Type : Adobe Acrobat Document
Chapter : IAHR World Congress Proceedings
Category : 36th Congress - The Hague (2015) ALL CONTENT
Article : Water engineering
Date Published : 28/08/2015
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