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Simple efficient algorithm (SEA) for shallow flows with shock wave on dry and irregular beds
Author(s) -
Zia Alireza,
Banihashemi Mohamad Ali
Publication year - 2007
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.1585
Subject(s) - discretization , shallow water equations , finite volume method , algorithm , simple (philosophy) , dimensioning , simple algorithm , term (time) , shock (circulatory) , mathematics , mathematical optimization , computer science , mechanics , mathematical analysis , engineering , medicine , philosophy , physics , epistemology , quantum mechanics , thermodynamics , aerospace engineering
Abstract An explicit Godunov‐type solution algorithm called SEA (simple efficient algorithm) has been introduced for the shallow water equations. The algorithm is based on finite volume conservative discretisation method. It can deal with wet/dry and irregular beds. Second‐order accuracy, in both time and space, is achieved using prediction and correction steps. A very simple and efficient flux limiting technique is used to equip the algorithm with total variation dimensioning property for shock capturing purposes. In order to make sure about the balance between the flux gradient and the bed slope, treatment of the source term has been done using a new procedure inspired mainly by the physical rather than mathematical consideration. SEA has been applied to one‐dimensional problems, although it can equally be applied to multi‐dimensional problems. In order to assess thecapability of proposed algorithm in dealing with practical applications, several test cases have been examined. Copyright © 2007 John Wiley & Sons, Ltd.