  We study decoupled numerical methods for multi-domain, multi-physics
applications. By investigating various stages of numerical approximation and
decoupling and tracking how the information is transmitted across the interface
for a typical multi-modeling model problem, we derive an approximate intrinsic
or inertial type Robin condition for its semi-discrete model. This new
interface condition is justified both mathematically and physically in contrast
to the classical Robin interface condition conventionally introduced for
decoupling multi-modeling problems. Based on the intrinsic or inertial Robin
condition, an equivalent semi-discrete model is introduced, which provides a
general framework for devising effective decoupled numerical methods. Numerical
experiments also confirm the effectiveness of this new decoupling approach.
