E.T. Kaar

Doctor of Philosophy, St. Edmund Hall, University of Oxford, Michaelmas Term 1991

Curvilinear Systems Modelling of Pollutant Transport in Shallow Waters

Summary

The subject of this thesis is the application of curvilinear systems to numerical modelling of pollutant transport in shallow flow domains of irregular shape, such as rivers, lakes and reservoirs. Boundary-fitted (curvilinear) approaches have received much attention over the past decade, because they allow coordinate lines to be coincident with the perimeter of the region of interest, so that the arbitrary shape of the flow domain is preserved exactly.

The curvilinear grid is generated as the solution of a coupled pair of Poissons equations, where the right hand side of the equations consists of forcing functions which control spacing of coordinate liens. This allows nodes to be concentrated in regions of interest, and stretched apart in other areas. The grid generation equations are solved as a boundary value problem in finite-difference form, using successive over-relaxation (SOR).

Prediction of the flow hydrodynamics is based on the depth-averaged Reynolds equations (often called the shallow water equations) which are expressed in curvilinear depth-averaged stream function / vorticity-transport form. The system effectively comprises two equations, which are discretised using finite-differences on a non-staggered mesh. The stream function equation is solved by SOR, and an alternating direction implicity (ADI) scheme is used for the vorticity-transport equation. Central differences are used throughout, except for the advection term in the vorticity-transport equation, which is solved using a weighted combination of upwind and central differences. Validation of the model is carried out against independent experimental and numerical data for the cases of a backward facing step in a rectangular channel and jet-forced flow in a circular reservoir. Experimental results are presented from a small scale physical model of the circular reservoir. These comparisons provide stringent tests for the stability and accuracy of the numerical scheme. Moreover, the amount of artificial viscosity introduced by the upwind differencing can be used.

Once the flow kinematics are established, the velocity field is used to drive the pollutant transport by means of a transformed depth-averaged species equation, where it is assumed that the pollutant is well-mixed over the depth. The species equation is discretised using finite- differences and solved with an explicit time-stepping scheme. Validation is carried out against experimental data from the physical model of the circular reservoir, in which the spread of dye is monitored by video camera.

(no thesis available)