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Time accurate local time stepping for the unsteady shallow water equations
Author(s) -
Crossley A. J.,
Wright N. G.
Publication year - 2005
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.956
Subject(s) - time stepping , euler equations , upwind scheme , shallow water equations , flow (mathematics) , finite volume method , euler's formula , mathematics , series (stratigraphy) , unsteady flow , term (time) , channel (broadcasting) , computer science , algorithm , geometry , mechanics , mathematical analysis , geology , physics , discretization , paleontology , computer network , quantum mechanics
Abstract Two time accurate local time stepping (LTS) strategies originally developed for the Euler equations are presented and applied to the unsteady shallow water equations of open channel flow. Using the techniques presented allows individual cells to be advanced to different points in time, in a time accurate fashion. The methods shown are incorporated into an explicit finite volume version of Roe's scheme which is implemented in conjunction with an upwind treatment for the source terms. A comparison is made between the results obtained using the conventional time stepping approach and the two LTS methods through a series of test cases. The results illustrate a number of benefits of using LTS which included reduced run times and improved solution accuracy. In addition it is shown how using an upwind source term treatment can be beneficial for flows dominated by the geometry. Copyright © 2005 John Wiley & Sons, Ltd.