Numerical Methods for Solution of the Shallow-Water Equations in Meteorology

摘要

The system of partial differential equations representing motion in a homogeneous, incompressible and nonviscous fluid in hydrostatic equilibrium with a free surface is dealt with. This system, referred to in meteorology as the shallow water equations system or the primitive barotropic equations system, provides an approximation to large scale weather prediction equations having the same numerical characteristics. Methods for solving this system with improved accuracy or high computational efficiency are studied. Several numberical aspects of this system quasilinear hyperbolic partial differential equations, viewed as a mixed initial boundary value problem, are highlighted. The long term behavior of the shallow water equations systems in the inviscid limit is related to the conservation of a number of integral invariants, in particular conservation of potential enstrophy. The paramount importance of well posed numerical boundary conditions as a prerequisite for the success of limited area integrations of the shallow water equations systems is shown.