Lateral Boundary Conditions for Quasisteady Atmospheric Flows.
Progress rept. 1 Jul-31 Dec 79,
PURDUE UNIV HAMMOND IN DEPT OF MATHEMATICAL SCIENCES
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The quasisteady model is extended to include lateral boundary conditions. The approach is to first assume a well-posed complete time-dependent problem, including boundary conditions it is stressed that to each boundary condition there should be associated a precise physical assumption. It is then shown that the quasisteady assumption can be applied consistently to both the partial differential equations and the boundary conditions, thereby obtaining a well-posed mathematical model with time scales suitable for large scale atmospheric flows. Three types of conditions are considered at the lateral boundaries 1 outflow, 2 inflow driven velocity is specified and is essentially independent of the internal flow, 3 inflow passive - inflow is created primarily by the internal flow configuration. The upper boundary conditions include the two derived in an earlier paper, the continuous and discontinous boundary conditions, and a third condition, which is designed to allow the flow to propagate independently of the height of the region. Numerical solutions are obtained for various test cases, and convergence of the calculations is demonstrated. One sees that, although the calculations are reasonable, both from a mathematical and physical standpoint, the various calculations differ from each other very significantly, both qualitatively and quantitatively. It is suggested, therefore, that the process of specifying and evaluating boundary conditions will proceed more efficiently if more physical understanding is obtained in regard to relatively simply flows, such as a wave entering a stationary flow at a lateral boundary.
- Atmospheric Physics
- Numerical Mathematics
- Fluid Mechanics