The modelling of the processes of advection and dispersion-diffusion is the
most crucial factor in solute transport simulations. It is generally appreciated
that the first order upwind difference scheme gives rise to excessive numerical
diffusion, whereas the conventional second order central difference scheme exhibits
severe oscillations for advection dominated transport, especially in regions
of high solute gradients or discontinuities. Higher order schemes have therefore
become increasingly used for improved accuracy and for reducing grid scale oscillations.
Two such schemes are the QUICK (Quadratic Upwind Interpolation for
Convective Kinematics) and TOASOD (Third Order Advection Second Order
Diffusion) schemes, which are similar in formulation but different in accuracy,
with the two schemes being second and third order accurate in space respectively
for finite difference models. These two schemes can be written in various
finite difference forms for transient solute transport models, with the different
representations having different numerical properties and computational efficiencies.
Although these two schemes are advectively (or convectively) stable,
it has been shown that the originally proposed explicit QUICK and TOASOD
schemes become numerically unstable for the case of pure advection. The stability
constraints have been established for each scheme representation based
upon the von Neumann stability analysis. All the derived schemes have been
tested for various initial solute distributions and for a number of continuous
discharge cases, with both constant and time varying velocity fields.
The 1-D QUICKEST (QUICK with Estimated Streaming Term) scheme is
third order accurate both in time and space. It has been shown analytically and
numerically that a previously derived quasi 2-D explicit QUICKEST scheme,
with a reduced accuracy in time, is unstable for the case of pure advection. The
modified 2-D explicit QUICKEST, ADI-TOASOD and ADI-QUICK schemes
have been developed herein and proved to be numerically stable, with the bility sta- region of each derived 2-D scheme having also been established. All these
derived 2-D schemesh ave been tested in a 2-D domain for various initial solute distributions with both uniform and rotational flow fields. They were further
tested for a number of 2-D continuous discharge cases, with the corresponding
exact solutions having also been derived herein.
All the numerical tests in both the 1-D and 2-D cases were compared with
the corresponding exact solutions and the results obtained using various other
difference schemes, with the higher order schemes generally producing more
accurate predictions, except for the characteristic based schemes which failed
to conserve mass for the 2-D rotational flow tests. The ADI-TOASOD scheme
has also been applied to two water quality studies in the U. K., simulating nitrate
and faecal coliform distributions respectively, with the results showing a
marked improvement in comparison with the results obtained by the second
order central difference scheme.
Details are also given of a refined numerical representation of flooding and
drying of tidal flood plains for hydrodynamic modelling, with the results showing
considerable improvements in comparison with a number of existing models
and in good agreement with the field measured data in a natural harbour study.
| Identifer | oai:union.ndltd.org:BRADFORD/oai:bradscholars.brad.ac.uk:10454/4344 |
| Date | January 1992 |
| Creators | Chen, Yiping |
| Publisher | University of Bradford, Department of Civil Engineering |
| Source Sets | Bradford Scholars |
| Language | English |
| Detected Language | English |
| Type | Thesis, doctoral, PhD |
| Rights | <a rel="license" href="http://creativecommons.org/licenses/by-nc-nd/3.0/"><img alt="Creative Commons License" style="border-width:0" src="http://i.creativecommons.org/l/by-nc-nd/3.0/88x31.png" /></a><br />The University of Bradford theses are licenced under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-nd/3.0/">Creative Commons Licence</a>. |
Page generated in 0.0035 seconds