Nonreflecting Boundary Conditions
If the boundary of a computational domain coincides with a true physical boundary, an appropriate boundary condition can generally be derived from physical principles and can be implemented in a numerical model with relative ease. It is, for example, easy to derive the condition that the fluid velocity normal to a rigid boundary must vanish at that boundary, and if the shape of the boundary is simple, it is easy to impose this condition on the numerical solution. More serious difficulties may be encountered if the computational domain terminates at some arbitrary location within the fluid. When possible, it is a good idea to avoid artificial boundaries by extending the computational domain throughout the entire fluid. Nevertheless, in many problems the phenomena of interest occur in a localized region, and it is impractical to include all of the surrounding fluid in the numerical domain. As a case in point, one would not simulate an isolated thunderstorm with a global atmospheric model just to avoid possible problems at the lateral boundaries of a limited domain. Moreover, in a fluid such as the atmosphere there is no distinct upper boundary, and any numerical representation of the atmosphere’s vertical structure will necessarily terminate at some arbitrary level.
KeywordsDispersion Relation Group Velocity Internal Gravity Wave Open Boundary Condition Advection Equation
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- 1.As discussed in Section 1.3.2, a well-posed problem is one in which a unique solution to a given partial differential equation exists and depends continuously on the initial- and boundary-value data.Google Scholar
- 2.The relation (8.29) is sometimes described as a dispersion relation for a pseudodifferential operator.Google Scholar
- 4.Here P is replaced by p/ρ0 to match the terminology in Section 7.3.2.Google Scholar