The numerical generating method for global homeomorphic grid from multi-dimensional towel-shaped reality region to square computational region is investigated. The numerical iterative method for multi-dimensional equal-parameter transformation is given. Its error analysis and the sufficient condition of numerical grid without overlapping is pressented. Finally, an example about two-dimensional non-overlapping numerical grid generation for Qiantang Estuary is shown.

For the need of numerical simulating the shallow-water bore, the Roe average method about the coefficient matrix of shallow-water wave equations is presented. Several freezing methods are used to treat the one dimensional shallow water wave equation for numerical examining with a dam breaking problem, numerical results show the superiority of the Roe average method in simulating the bore.