8
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 aglobai atmospheric model just to avoid possible problems at
the lateral boundaries of a Iimited 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.
When the computational domain is terminated at an arbitrary location within
a larger body of fluid, the conditions imposed at the edge of the domain are intended to mimic the presence of the surrounding fluid. The boundary conditions
should therefore allow outward-traveling disturbances to pass through the boundary without generating spurious reflections that propagate back toward the interior. Boundary conditions designed to minimize spurious backward reflection
are known as nonrejlecting, open, wave-permeable, or radiation boundary conditions. The terminology "radiation boundary condition" is due to Sommerfeld
D. R. Durran, Numerical Methods for Wave Equations in Geophysical Fluid Dynamics
© Springer Science+Business Media New York 1999
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 aglobai atmospheric model just to avoid possible problems at
the lateral boundaries of a Iimited 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.
When the computational domain is terminated at an arbitrary location within
a larger body of fluid, the conditions imposed at the edge of the domain are intended to mimic the presence of the surrounding fluid. The boundary conditions
should therefore allow outward-traveling disturbances to pass through the boundary without generating spurious reflections that propagate back toward the interior. Boundary conditions designed to minimize spurious backward reflection
are known as nonrejlecting, open, wave-permeable, or radiation boundary conditions. The terminology "radiation boundary condition" is due to Sommerfeld
D. R. Durran, Numerical Methods for Wave Equations in Geophysical Fluid Dynamics
© Springer Science+Business Media New York 1999