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Multi-scale simulations of liquid metal systems 367

Fig. 7.2 “Decomposition” and “overlapped” approaches to multiscale coupling. In order to
construct a model in which a “fine” model of a specific region (in gray) is used in concert with a
coarse model of the rest of the system, the “domain decomposition” approach (left) consists in
removing the gray region from the system-scale model. Alternatively, in the “overlapping”
approach (right), this region is left in the STH model: the role of the coupling algorithm is
therefore to overlay the STH results obtained in the gray region with those obtained by the finer
calculation.

the overlapped domain (and not only at its boundaries). Such issues are not present when
the domain decomposition scheme is used, since both domains are completely separated
and communicate through the coupling interfaces.
Because of this added complexity, an overlapped coupling is inherently harder to imple-
ment and verify than a decomposition coupling: while an error in the coupling algorithm
will usually result in easily visible defects in a decomposition coupling, an error in an
overlapped coupling will usually result in the spurious use of system-scale results in the
overlapped domain. This will in turn lead to a much less visible degradation of the
coupled solution, which may be hard to notice or track down.

However, an overlapped coupling will usually avoid some of the tight coupling issues asso-
ciated with the decomposition approach. In particular, in an overlapped coupling, the pres-
sure field calculations performed by the system and CFD codes are not tightly coupled, and
can be implemented using source terms (see Section 7.2.2). For this reason, an overlapped
coupling algorithm may be simpler to implement from a numerical point of view.
Finally, in the overlapped approach, the same system-scale model used for coupled calcu-
lations is self-sufficient, so that it can be used to perform stand-alone calculations. This
capability can be used to provide an initial state for the coupled calculation without using
a different STH model (as coupled calculations are usually initialized from a STH steady
state); it also allows one to compare easily the differences between a coupled calculation and
its “original” STH calculation. A domain decomposition coupling may implement the same
functionality by automating the “removal” of the overlapped part of the STH input deck
during coupled calculation: for instance, in the ATHLET/ANSYS CFX domain decompo-
sition coupling scheme, a complete ATHLET input deck is used for both stand-alone and
coupled calculations, but the overlapped ATHLET domain is deactivated during coupled
time steps.