fluid
The St Venant Equations
Dr P A Sleigh
Dr I M Goodwill
School of Civil Engineering,
University of Leeds
March 2000
1
THE DERIVATION OF THE CONTINUITY EQUATION ...........................................................................................1
2
THE DERIVATION OF THE DYNAMIC OR MOMENTUM EQUATION. ...............................................................2
3
THE SOLUTION OF THE ST VENANT EQUATIONS .................................................................................................4
3.1
AN MORE CONVENIENT FORM OF THE EQUATIONS ...........................................................................................................4
3.2
A DIVERSION …. .............................................................................................................................................................5
3.3
THE CHARACTERISTIC FORM OF THE ST VENANT EQUATIONS .........................................................................................5
3.4
THE MEANING OF THE CHARACTERISTIC FORM ................................................................................................................7
3.5
AN EXAMPLE COMPUTATION USING THE CHARACTERISTIC EQUATIONS ...........................................................................8
3.6
THE DOMAIN OF DEPENDENCE AND ZONE OF INFLUENCE .................................................................................................9
3.7
A FIRST NUMERICAL METHOD OF SOLUTION ....................................................................................................................9
3.7.1
The Staggered Grid Method .................................................................................................................................10
3.8
STABILITY AND ACCURACY ..........................................................................................................................................11
3.9
A SECOND NUMERICAL SOLUTION
Dr P A Sleigh
Dr I M Goodwill
School of Civil Engineering,
University of Leeds
March 2000
1
THE DERIVATION OF THE CONTINUITY EQUATION ...........................................................................................1
2
THE DERIVATION OF THE DYNAMIC OR MOMENTUM EQUATION. ...............................................................2
3
THE SOLUTION OF THE ST VENANT EQUATIONS .................................................................................................4
3.1
AN MORE CONVENIENT FORM OF THE EQUATIONS ...........................................................................................................4
3.2
A DIVERSION …. .............................................................................................................................................................5
3.3
THE CHARACTERISTIC FORM OF THE ST VENANT EQUATIONS .........................................................................................5
3.4
THE MEANING OF THE CHARACTERISTIC FORM ................................................................................................................7
3.5
AN EXAMPLE COMPUTATION USING THE CHARACTERISTIC EQUATIONS ...........................................................................8
3.6
THE DOMAIN OF DEPENDENCE AND ZONE OF INFLUENCE .................................................................................................9
3.7
A FIRST NUMERICAL METHOD OF SOLUTION ....................................................................................................................9
3.7.1
The Staggered Grid Method .................................................................................................................................10
3.8
STABILITY AND ACCURACY ..........................................................................................................................................11
3.9
A SECOND NUMERICAL SOLUTION