140
ERIC BLAYO AND LAURENT DEBREU
the Flather condition (14) corresponds to specifying the value of
the incoming characteristic of the shallow water system, fulfilling
the criterion (24) with B = Id the identity operator.
absorbing conditions are closely linked to incoming characteristic
variables, and the conditions proposed by McDonald (2002, 2003)
and Nycander and D¨ o¨ os (2003) can be written under the form (24).
characteristic waves amplitudes methods do also meet the preceding point of view.
since relaxation methods are not local conditions, the criterion
(24) does not apply directly. However, it is obvious from (11) that
the transition from φ to φ
ext is smooth as soon as the additional
domain Ω s is large enough. Similarly the problem of specifying
incoming characteristics and evacuating outcoming characteristics
at the open boundary is treated implicitely: the values of the
incoming characteristics are computed within Ω s , using the relaxed
solution, while the outgoing characteristics are not directly affected
when reaching Γ but are relaxed in Ω s towards their corresponding
external values, and damped by the increased dissipation.
Details on these aspects, as well as an application of the criterion (24) to
shallow-water and primitive equations systems, are discussed in Blayo
and Debreu (2005).
3.3
Some practical remarks
It is important to note that we discussed here only the continuous
form of the equations. However discretized models contain spurious numerical modes, which nature is different from that of physical modes, and which have to be handled by the OBCs. Therefore, once the continuous form of the OBCs is chosen, one has
to perform some specific work in order to adapt their numerical
implementation to the numerical schemes of the model. This difficulty is probably also a reason for the efficiency of relaxation and
radiation-relaxation methods, which tend to automatically damp
these non-physical modes.
Incoming information is entirely given by the external solution φ
ext .
Therefore the quality of these data is of course an important point
in the performance of a regional modelling system.
Another important practical aspect in a regional modelling system
is the initialization problem. The initial condition is generally built
ERIC BLAYO AND LAURENT DEBREU
the Flather condition (14) corresponds to specifying the value of
the incoming characteristic of the shallow water system, fulfilling
the criterion (24) with B = Id the identity operator.
absorbing conditions are closely linked to incoming characteristic
variables, and the conditions proposed by McDonald (2002, 2003)
and Nycander and D¨ o¨ os (2003) can be written under the form (24).
characteristic waves amplitudes methods do also meet the preceding point of view.
since relaxation methods are not local conditions, the criterion
(24) does not apply directly. However, it is obvious from (11) that
the transition from φ to φ
ext is smooth as soon as the additional
domain Ω s is large enough. Similarly the problem of specifying
incoming characteristics and evacuating outcoming characteristics
at the open boundary is treated implicitely: the values of the
incoming characteristics are computed within Ω s , using the relaxed
solution, while the outgoing characteristics are not directly affected
when reaching Γ but are relaxed in Ω s towards their corresponding
external values, and damped by the increased dissipation.
Details on these aspects, as well as an application of the criterion (24) to
shallow-water and primitive equations systems, are discussed in Blayo
and Debreu (2005).
3.3
Some practical remarks
It is important to note that we discussed here only the continuous
form of the equations. However discretized models contain spurious numerical modes, which nature is different from that of physical modes, and which have to be handled by the OBCs. Therefore, once the continuous form of the OBCs is chosen, one has
to perform some specific work in order to adapt their numerical
implementation to the numerical schemes of the model. This difficulty is probably also a reason for the efficiency of relaxation and
radiation-relaxation methods, which tend to automatically damp
these non-physical modes.
Incoming information is entirely given by the external solution φ
ext .
Therefore the quality of these data is of course an important point
in the performance of a regional modelling system.
Another important practical aspect in a regional modelling system
is the initialization problem. The initial condition is generally built