Coupling (Coupled Analysis) — CAE Glossary

Basically, we're in the world of multiphysics. When multiple physical phenomena like structures, fluids, heat, and electromagnetic fields interact with each other, solving them together is coupled analysis. Single-physics analysis solves only one physical field, but in reality, products involve multiple interacting physics. For example, an engine piston deforms due to combustion gas pressure (fluid) and is simultaneously exposed to high temperature (thermal). If you solved these separately, you wouldn't capture the real behavior.

Good question. One-way coupling (One-way coupling) passes the result from field A to field B, but doesn't return the result from B back to A. In arrow notation: A → B, one direction only.

Exactly. Two-way coupling (Two-way coupling) alternates data exchange between A and B and repeats until both solutions converge. FSI (fluid-structure interaction) is a clear example: fluid applies pressure to the structure causing deformation → the deformed shape changes the flow field → a new pressure distribution acts on the structure. You repeat this loop until it converges.

The decision criterion is "whether reverse-direction effects significantly change the result." For example, in thermal stress on electronic boards, deformation is on the order of micrometers and barely affects the temperature field, so one-way is sufficient. But for an aircraft wing, the wing deflects from aerodynamic load, changing the angle of attack and thus the lift distribution—that requires two-way coupling. Two-way is computationally far more expensive, so the engineering rule is: use one-way if it's adequate.

There are two main approaches.

Right, that's the weakness of monolithic. In practice, partitioned (Partitioned) is overwhelmingly more common. The partitioned approach solves each physical field with its own dedicated solver and exchanges data at the interface. You can combine field-specific solvers like Fluent for fluids and Abaqus for structures. Plus, you can optimize mesh density and time step for each field independently.

Yes. Partitioned coupling introduces time lag in data exchange at the interface, so for strongly coupled problems (where field interaction is very strong), convergence can be difficult. A classic example is the "added-mass effect"—when a lightweight structure oscillates in a dense fluid. The partitioned approach can become unstable. In such cases, you increase the number of sub-iterations (interface iteration) or use relaxation techniques like Aitken acceleration.

Common industrial applications include:

The interface compatibility conditions are essentially two: kinematic (continuity of displacement/velocity) and dynamic (force balance). From the fluid side, the interface is a moving wall, so the fluid mesh must follow the structure's displacement. The ALE method is commonly used for this. On the structure side, surface traction (pressure) from the fluid is applied. Since fluid and structure meshes often don't match, the accuracy of interface mapping (interpolation) is critical.

In many cases, it's numerically less difficult than FSI. Thermal-structural coupling involves the temperature field $T$ and displacement field $\mathbf{u}$. The basic mechanism is:

A typical case is metal plastic deformation. In forging and stamping, plastic deformation generates enormous heat, raising temperature, which lowers the material's yield stress, making it easier to deform further. This "deformation → heat generation → softening → more deformation" feedback loop requires two-way coupling for accuracy. Friction stir welding (FSW) is another example.

Here's a practical checklist for starting coupled analysis: