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On the diffusive wave approximation of the shallow water equations†

Published online by Cambridge University Press:  01 October 2008

R. ALONSO ,
M. SANTILLANA  and
C. DAWSON
R. ALONSO
Affiliation:
Department of Mathematics, University of Texas Austin, Austin, TX 78712, USA
M. SANTILLANA
Affiliation:
Institute for Computational Engineering and Sciences, University of Texas Austin, Austin, TX 78712, USA email: mauricio@ices.utexas.edu
C. DAWSON
Affiliation:
Institute for Computational Engineering and Sciences, University of Texas Austin, Austin, TX 78712, USA email: mauricio@ices.utexas.edu
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Abstract

In this paper, we study basic properties of the diffusive wave approximation of the shallow water equations (DSW). This equation is a doubly non-linear diffusion equation arising in shallow water flow models. It has been used as a model to simulate water flow driven mainly by gravitational forces and dominated by shear stress, that is, under uniform and fully developed turbulent flow conditions. The aim of this work is to present a survey of relevant results coming from the studies of doubly non-linear diffusion equations that can be applied to the DSW equation when topographic effects are ignored. In fact, we present proofs of the most relevant results existing in the literature using constructive techniques that directly lead to the implementation of numerical algorithms to obtain approximate solutions.

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Type
Papers
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European Journal of Applied Mathematics , Volume 19 , Issue 5 , October 2008 , pp. 575 - 606
Copyright
Copyright © Cambridge University Press 2008

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