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Is My Coupled Field Model Truly Coupled, or is it a One-Sided Relationship?

Coupled Field Model CFD FEA | FEA or CFD Consulting
November 20, 2015 By: Patrick Cunningham

What is a coupled field problem anyway? When we use the term coupled field in the engineering world, we are referring to a system that is affected by more than one physical phenomena. Coupled field problems can include the combinations like thermal-structural, fluid-structural, thermal- fluid, and piezoelectric, to name a few. 

Consider a thermal-structural response, for example. You have thermal loads. Those thermal loads result in temperature distribution. That temperature delta results in thermal strain in your structural model. The result? Unless someone is kind enough to provide you with some temperatures, you will need to run both a thermal and a structural analysis. 

This leads to another question: Can you get away with modeling the thermal and structural fields separately, or, does the response of one field affect the other and vice versa?   The answer to this question will govern how you approach the problem.

A loosely coupled system (in this example) is one where the temperature result is independent of the structural deformation but adds a thermal strain component to the structural result. This scenario is often referred to a one way coupled problem. While the thermal model is independent, the structural model sits idly waiting for temperatures to apply. 

A closely coupled field problem is one where the responses of the two fields are dependent on each other. For example consider a thermal switch that is initially open and closes as components heat up and come into contact. Once in contact, the switch will conduct heat across the connection which affects the temperature distribution and thus the deformation caused by the thermal expansion. In this scenario, the two fields share equal roles in the system response. 

There are two methods that can be used to model a closely coupled system. The first is a direct approach where the same model is used to generate both solutions. In this case, the finite element formulations must include both thermal and structural degrees of freedom. 

Another approach to solving closely coupled systems is to use two separate models and update both models for each load increment applied. This approach is typical for FSI analyses (Fluid-Structure Interaction) where the models share very little in common in the types of elements and solvers used. What they do share is the same locations at the interfaces between the fluid and the solid. Interpolation tools are used to map the fluid response (pressure, temperature, heat flux, etc.) onto the structural elements.  The deformed shape from the structural model is used to update the flow volume of the fluid model for the next load increment. The example in Figures 1 and 2 (above) illustrates an FSI approach in the analysis of an impeller. The fluid and solid models are solved independently but each model is updated with the response of the other.

So the first question you need to answer when dealing with a coupled field situation is how closely will the fields will be coupled. The answer will determine how you will need to model the system, and often, which tools you will need to use.