NESTING OCEAN MODELS
141
by interpolation of a larger scale solution, which is not perfectly
consistent with the local model. This can yield an adjustment
phase which can be quite long, and which pollutes the model solution. A way to avoid (or limit) this problem is to add some relevant
constraints in the computation of the initial condition, as done for
instance by Auclair et al. (2000) using an inverse approach. This
aspect is presently the subject of numerous studies.
4.
Two-way interaction
4.1
Two-way nesting
As explained in §2, the usual two-way method differs from the preceding one-way method by the addition of an update procedure. This
supplementary step aims at improving u ext by modifying it locally using
u loc . This retroaction from the local model onto the external model is
performed every external model timestep, or less frequently. The update
operator generally replaces the values of u ext at gridpoints located in Ω loc
by copying the corresponding values of u loc , eventually after some time
and space averaging. Such an update is quite brutal, and in particular
does not ensure the balance of mass and tracers fluxes through Γ. For
example,
Γ
U loc .n =
Γ
U ext .n, where U denotes the velocity. That is
why a flux correction step is often added, which generally modifies u loc
to distribute the flux misfit all along Γ, to get finally a local solution u ∗
loc
which is in flux balance with u ext .
The two-way method generally decreases the difficulties that can be
encountered by the one-way method (in particular the instabilities along
Γ), and seems to improve the model solution. That is why it is recommended to use it as far as possible rather than one-way interaction.
However, it is clear that the solution provided by this usual two-way
nesting is not solution of the original problem (5): before the flux correction step, the connection between u ext and u loc is not differentiable,
because their fluxes are not balanced; after the flux correction step, the
connection is no more continuous because u loc has been modified into
u ∗
loc , which in addition does not satisfy any longer the local model equations (1).
4.2
Full coupling - Schwarz methods
Obtaining a solution of the original problem (5) is much more difficult
and expensive than what is done in the above usual algorithms. This is
mainly due to the fact that, since the local and external model equations
are different, their domains of application should not overlap. Therefore
141
by interpolation of a larger scale solution, which is not perfectly
consistent with the local model. This can yield an adjustment
phase which can be quite long, and which pollutes the model solution. A way to avoid (or limit) this problem is to add some relevant
constraints in the computation of the initial condition, as done for
instance by Auclair et al. (2000) using an inverse approach. This
aspect is presently the subject of numerous studies.
4.
Two-way interaction
4.1
Two-way nesting
As explained in §2, the usual two-way method differs from the preceding one-way method by the addition of an update procedure. This
supplementary step aims at improving u ext by modifying it locally using
u loc . This retroaction from the local model onto the external model is
performed every external model timestep, or less frequently. The update
operator generally replaces the values of u ext at gridpoints located in Ω loc
by copying the corresponding values of u loc , eventually after some time
and space averaging. Such an update is quite brutal, and in particular
does not ensure the balance of mass and tracers fluxes through Γ. For
example,
Γ
U loc .n =
Γ
U ext .n, where U denotes the velocity. That is
why a flux correction step is often added, which generally modifies u loc
to distribute the flux misfit all along Γ, to get finally a local solution u ∗
loc
which is in flux balance with u ext .
The two-way method generally decreases the difficulties that can be
encountered by the one-way method (in particular the instabilities along
Γ), and seems to improve the model solution. That is why it is recommended to use it as far as possible rather than one-way interaction.
However, it is clear that the solution provided by this usual two-way
nesting is not solution of the original problem (5): before the flux correction step, the connection between u ext and u loc is not differentiable,
because their fluxes are not balanced; after the flux correction step, the
connection is no more continuous because u loc has been modified into
u ∗
loc , which in addition does not satisfy any longer the local model equations (1).
4.2
Full coupling - Schwarz methods
Obtaining a solution of the original problem (5) is much more difficult
and expensive than what is done in the above usual algorithms. This is
mainly due to the fact that, since the local and external model equations
are different, their domains of application should not overlap. Therefore