Development of a High Resolution Numerical Scheme Based on Quasi-Characteristics Applicable to Water Quality Modelling
This report was produced for the Urban Water Research Association of Australia, a now discontinued research program.
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Report No UWRAA 96
July 1995
SYNOPSIS
Many deterministic water quality models are based on the solution of the one-dimensional advective-diffusion equation. This equation has been shown to be sophisticated enough to successfully simulate a wide range of problems, yet simple enough to be amenable for solutions using modern digital computers.
In urban channels, where the catchment response is very rapid, steep concentration profiles are usually observed. There are difficulties associated with solving the advective-diffusion equation when there are steep gradients in the concentration profile. Many of the existing water quality models are unable to accurately model rapid catchment responses.
A truly robust universally applicable high resolution technique for solving the one-dimensional advective-diffusion equations applicable to modelling water quality in urban watercourses is developed. The high resolution model is based on Quasi-characteristics, a new method for solving partial differential equations. The performance of this model was assessed by comparing the results from the model against the results from other numerical schemes for solving the advective-diffusion equation. These included standard finite difference schemes, schemes for solving conservative laws and a quasi-analytical scheme based on the Laplace transform.
Models based on the Quasi-characteristic scheme with shape preserving cubic Hermite interpolation are shown to be robust and consistently provides accurate results. It is simple to implement and suitable for a whole range of problems.
Go to the Urban Water Research Association of Australia catalogue