Uoane, Tumelo R.A.2011-06-232011-06-232011-06-23http://hdl.handle.net/10539/10179The lattice Boltzmann (LB) method has become an e ective numerical technique for computational uid dynamics (CFD). The method is based on gas kinetic theory and is used as an alternative numerical method to simulate shallow water equations (SWEs). In this work, an overview of the Shallow Water LB method will be presented and the stability of this approach will be investigated. The stability structure will be used as a guideline to determine the stability of LB equations applied to SWEs. For instant some of the parameters in the LB equations are adjusted based on the stability structure. With this method, stable LB models are prescribed. To verify the stability theory, computational results for a few examples used in the literature are presented.enThesis