NDLI: Computation of the Shallow Water Equations Using the Unified Coordinates

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Hui, W. H. Koudriakov, S.
Copyright Year	2002
Abstract	Two general coordinate systems have been used extensively in computational fluid dynamics: the Eulerian and the Lagrangian. The Eulerian coordinates cause excessive numerical diffusion across flow discontinuities, slip lines in particular. The Lagrangian coordinates, on the other hand, can resolve slip lines sharply but cause severe grid deformation, resulting in large errors and even breakdown of the computation. Recently, in the spirit of the arbitrary Lagrangian--Eulerian (ALE) approach, W.H. Hui, P.Y. Li, and Z.W. Li, [J. Comput. Phys., 153 (1999), pp. 596--637] have introduced a unified coordinate system which moves with velocity hq , q being the velocity of the fluid particle. It includes the Eulerian system as a special case when h=0, and the Lagrangian when h=1, and was shown for the two-dimensional Euler equations of gas dynamics to be superior to both Eulerian and Lagrangian systems. The main purpose of this paper is to adopt this unified coordinate system to solve the shallow water equations. It will be shown that computational results using the unified system are superior to existing results based on either the Eulerian system or Lagrangian system in that it (a) resolves slip lines sharply, especially for steady flow, (b) avoids grid deformation and computation breakdown in Lagrangian coordinates, and (c) avoids spurious flow produced by Lagrangian coordinates.
Starting Page	1615
Ending Page	1654
Page Count	40
File Format	PDF
ISSN	10648275
DOI	10.1137/S1064827500367415
e-ISSN	10957197
Issue Number	5
Volume Number	23
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2002-01-01
Access Restriction	Subscribed
Subject Keyword	Lagrangian description two-dimensional shallow water equations Eulerian description spurious vorticity due to Lagrangian description Nonlinear first-order hyperbolic equations unified description slip lines Water waves, gravity waves; dispersion and scattering, nonlinear interaction
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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