Weak coupling strong coupling and co-simulation

Coupling between two physical systems gives an idea of the influence they both have upon each other. It is a measure of how strongly changes in one system affect the other, and vice versa. In numerical terms, there is an equivalent notion, which consists in managing how closely two software packages (which are simulating different physical phenomena) interact when they are co-simulated.

Weak coupling

weak coupling

Putting this in the context of 1D/CFD co-simulation, the studies primarily involve fluid-structure interactions (here, represented by the 1D model). The coupling is therefore said to be weak when the dynamics of the fluid domain and that of the 1D system are significantly different.

This makes it possible to employ less numerically expensive methods while co-simulating the models. For example, one can reduce one of the models, simplifying it before it is interfaced with the other model. If the coupling is weak, this can be achieved without affecting the overall system’s dynamics.

Figure 27: Model reduction by static characterization (using tabulated data, for instance) is a way of implementing weak coupling

Another possibility is the use of relaxed coupling. This implies running whole simulations on one model, then using its outputs as inputs of the other system, which then simulates, and provides its outputs to the first, and so on.

An example of relaxed coupling is that of the thermal model of heat diffusion diffusion  in a disk clutch, which can be coupled by relaxation with a mechanical model of the clutch system. The dissipated heat computed by the mechanical model over a cycle is the source term of the thermal model. The temperature field on the disk alters the friction coefficient, which is used as a parametric input of the mechanical model.

Strong coupling

strong coupling

Coupling is said to be strong when the dynamics inherent in both systems are of the same order of magnitude. In this case, it is impossible to uncouple both systems – any changes made to the numerical representation of either system will affect the dynamics of the global (combined) system, meaning that it would no longer be representative.

Figure 28: An illustration of strong coupling: both phenomena (and both models) are highly dependent of each other

On the numerical level, there is no choice but to couple the solvers “strongly”, meaning that they exchange outputs at every time step. Of course, the exchange of outputs happens in both directions, as any alteration in the state of one system will have significant effects on the other.

An example of strong coupling is that of an injector nozzle model coupling a mechanical model of needle with a hydrodynamics model of fuel flow through the nozzle.

Note

In reality, the nature of the studies being conducted – mainly hydraulics, hydraulic component design and fuel injection – means that the vast majority of use-cases for 1D/3D CFD co-simulation will involve strong coupling.