Developmentof a High Resolution Numerical Scheme Based on Quasi-characteristics applicableto Water Quality Modelling

ReportNo WSAA 96

July 1995

SUMMARY

Manydeterministic water quality models are based on the solution of theone-dimensional advective-diffusion equation. This equation has been shown tobe sophisticated enough to successfully simulate a wide range of problems, yetsimple enough to be amenable for solutions using modern digital computers.

Inurban channels, where the catchment response is very rapid, steep concentrationprofiles are usually observed. There are difficulties associated with solvingthe advective-diffusion equation when there are steep gradients in theconcentration profile. Many of the existing water quality models are unable toaccurately model rapid catchment responses.

Atruly robust universally applicable high resolution technique for solving theone-dimensional advective-diffusion equations applicable to modelling waterquality in urban watercourses is developed. The high resolution model is basedon Quasi-characteristics, a new method for solving partial differentialequations. The performance of this model was assessed by comparing the resultsfrom the model against the results from other numerical schemes for solving theadvective-diffusion equation. These included standard finite differenceschemes, schemes for solving conservative laws and a quasi-analytical schemebased on the Laplace transform.

Modelsbased on the Quasi-characteristic scheme with shape preserving cubic Hermiteinterpolation are shown to be robust and consistently provides accurateresults. It is simple to implement and suitable for a whole range of problems.

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