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Finite-Volume Multi-Stage Scheme for Advection-Diffusion Modeling in Shallow Water Flows

Published online by Cambridge University Press:  31 August 2011

W.-D. Guo ,
J.-S. Lai ,
G.-F. Lin ,
F.-Z. Lee  and
Y.-C. Tan
W.-D. Guo
Affiliation:
Taiwan Typhoon and Flood Research Institute, National Applied Research Laboratories, Taipei, Taiwan 10093, R.O.C.
J.-S. Lai*
Affiliation:
Hydrotech Research Institute, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
G.-F. Lin
Affiliation:
Department of Civil Engineering, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
F.-Z. Lee
Affiliation:
Department of Bioenvironmental Systems Engineering, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
Y.-C. Tan
Affiliation:
Department of Bioenvironmental Systems Engineering, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
*
**Research Fellow, corresponding author
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Abstract

This paper adopts the finite-volume multi-stage (FMUSTA) scheme to the two-dimensional coupled system combining the shallow water equations and the advection-diffusion equation. For the convection part, the numerical flux is estimated by adopting the FMUSTA scheme, where high order accuracy is achieved by the data reconstruction using the monotonic upstream schemes for conservation laws method. For the diffusion part, the evaluations of first-order derivatives are solved via the method of Jacobian transformation. The hydrostatic reconstruction method is employed for treatment of source terms. The overall accuracy of resulting scheme is second-order both in time and space. In addition, the scheme is non-oscillatory and conserves the pollutant mass during the transport process. For scheme validation, six advection and diffusion transport tests are simulated. The influences of the grid spacing and limiters on the numerical performance are also discussed. Furthermore, the scheme is employed in the simulation of suspended sediment transport in natural-irregular river topography. From the satisfactory agreements between the simulated results and the field measured data, it is demonstrated that the proposed FMUSTA scheme is practically suitable for hydraulic engineering applications.

Keywords

Finite-volume multi-stage schemeShallow water equationsAdvection-diffusion equationMonotonic upstream schemes for conservation laws methodHydrostatic reconstruction method
Type
Articles
Information
Journal of Mechanics , Volume 27 , Issue 3 , September 2011 , pp. 415 - 430
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2011

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