What is Ansys System Coupling?

A framework that runs separate solvers — fluid, structural and others — together, exchanging interface forces, displacements or temperatures to perform coupled analysis. Each solver's full capability is retained; the order of data transfer, number of iterations and relaxation settings determine accuracy and run time.

Why do coupling iterations diverge?

When the structure is light and the fluid heavy (large added-mass ratio), the displacement correction driven by fluid force overshoots and grows each iteration. In the model problem, unrelaxed iterations diverged once the added-mass ratio exceeded 2. Relaxation that scales down the correction restores convergence.

How is the relaxation factor chosen?

A fixed value is more stable the smaller it is, but needs more iterations. In the model problem with a maximum added-mass ratio of 50, even the best fixed value took 95 iterations, whereas Aitken relaxation, which adjusts the factor from successive corrections, converged in 35. Many coupling tools offer such adaptive options.

Coupling Strategy with Ansys System Coupling

Category: Coupled Analysis | Revised 2026-09-30

CAE visualization for system coupling strategies theory - technical simulation diagram

Ansys System Coupling Strategy

Concept: linking separate solvers

Overview

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I set up fluid–structure coupling with System Coupling, but it diverges within a few steps. Where should I start?

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Start with coupling iterations and relaxation. In partitioned coupling, the fluid solver computes forces and passes them to the structure, which computes displacement and passes it back, repeated several times within each time step (coupling iterations). With a light structure in heavy fluid, the corrections overshoot and grow until the run diverges. The basic remedy is relaxation — taking only part of each correction.

One time step

The fluid solver solves with the current interface shape and computes interface forces (pressure and shear).
Forces are mapped to the structural mesh and the structural solver computes displacement.
Displacement is relaxed, returned to the fluid side and the fluid mesh is moved.
Repeat 1–3 until changes in force and displacement are small enough, then advance.

Relaxation formulas

$$ x^{k+1} = x^k + \omega\,\big(g(x^k) - x^k\big) $$

$$ \omega^{k+1} = -\omega^k\,\frac{(\mathbf{r}^k)^{\mathsf T}(\mathbf{r}^{k+1} - \mathbf{r}^k)}{\lVert \mathbf{r}^{k+1} - \mathbf{r}^k \rVert^2}, \qquad \mathbf{r}^k = g(x^k) - x^k $$

$g$ is one pass through fluid and structure, and $\omega$ the relaxation factor (0–1); $\omega = 1$ means no relaxation. The second formula is Aitken's method, which sets the next factor automatically from how the correction (residual $\mathbf{r}$) changed between iterations.

Coffee Break Trivia

The added-mass barrier

In the 2000s it was clearly shown that partitioned coupling struggles when the structure is about as light as the surrounding fluid — blood in vessels, thin plates in water, air around light membranes. The cause is the added-mass effect: the force needed to move the fluid exceeds the structure's own inertia. Smaller time steps don't help and can even make things worse. This drove widespread adoption of smarter acceleration methods such as Aitken relaxation and quasi-Newton schemes (e.g. IQN-ILS).

Worked example: iterations on a model problem

A linear model problem $x = c - R\,x$ with the interface displacement split into 20 modes, the added-mass ratio of mode i being $r_{max}/i$ (long waves couple most strongly). Coupling iterations were counted until the error fell below one part per million:

Max added-mass ratio	No relaxation	ω = 0.5	ω = 0.1	Best fixed ω	Aitken
0.5	18	19	125	8 (ω=0.79)	8
2	diverges	17	114	18 (ω=0.49)	12
10	diverges	diverges	81	48 (ω=0.16)	22
50	diverges	diverges	diverges	95 (ω=0.037)	35

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I thought a small relaxation factor was the safe choice, but the iteration count explodes.

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Right. ω = 0.1 takes 125 iterations when the added mass is small and diverges when it is large. A fixed value must be small enough for the most strongly coupled mode, which slows the weakly coupled ones. Aitken adjusts the factor every iteration and needed only 35 even at a ratio of 50. Real tools often offer such adaptive schemes or quasi-Newton methods, so they are worth trying first when a run diverges. Keep in mind this is a linear model problem; real counts and optimal values will differ.

Setting up

Checklist

Confirm each solver converges alone first; settings that fail standalone won't work coupled.
Check that mapping between interface meshes conserves total force.
Define convergence criteria for coupling iterations (changes in force and displacement) and log whether each step meets them.
For large added-mass ratios, use adaptive relaxation or quasi-Newton methods.
Decide whether weak (non-iterative) coupling suffices by comparing once with strong coupling, as in strong versus weak coupling.

Thinking about run time

One iteration = one pass of each solver: five coupling iterations make each step roughly five times as expensive.
Inner iterations: within coupling iterations, fewer inner solver iterations often suffice as long as the whole converges.

Coffee Break Trivia

“A smaller time step made it diverge”

Coupled fluid–structure runs were unstable, so the time step was halved — and the run diverged sooner. This is common when added-mass effects are strong: a smaller step increases the fluid reaction relative to how far the structure can move per step, making partitioned iterations less stable. The fluid-only instinct that smaller steps stabilise things backfires. Revisit the relaxation method or coupling scheme (strong coupling, quasi-Newton or monolithic) rather than the step size.

Common mistakes

Mistakes and fixes

Mistake	Effect	Fix
Starting without relaxation	Divergence with large added mass	Add relaxation or adaptive schemes
Over-small relaxation	Huge iteration counts	Aitken or quasi-Newton
Shrinking the step to stabilise	Less stable	Revisit the scheme
Not checking mapping conservation	Force or energy drift	Compare interface totals
Not logging coupling convergence	Advancing unconverged	Check residuals each step

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I'd like to learn more about coupling methods.

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Method differences are covered in partitioned versus monolithic coupling and staggered coupling, convergence criteria in convergence of coupled analyses, interface data transfer in mapping between dissimilar meshes, and whether to iterate at all in strong versus weak coupling.

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