Numerical Solutions to the Shallow Water Equations as Applied to a Local Meteorological Forecast Problem

摘要

An initial-boundary value problem comprised of a coupled system of three nonlinear, nonhomogeneous, hyperbolic first order partial differential equations is solved by numerical methods. The equations arise in geophysical fluid dynamics and describe the two-dimensional flow of a shallow, inviscid, homogeneous, incompressible fluid which is in hydrostatic balance. Their solution is used to describe the time evolution of winds at the earth's surface. The solution is obtained numerically using a first order in time, second order in space finite difference scheme which is capable of simulating flow over steep topography. Results indicate that the model produces satisfying mathematical solutions to the problem. However, it has difficulty producing useful meteorological wind forecasts when the flow is dominated by factors not included in it, most notably thermal and frictional effects. If these forces are secondary, the model is capable of providing useful wind forecasts.