Verification of Coupled Codes
Coupling separately verified codes introduces new errors at the interface; the coupled system needs its own verification.
The Whole Is a New Problem
Multiphysics simulations couple codes that each solve part of the problem: a plasma code with a structural code, a neutronics code with a thermal code. Verifying each code separately is necessary but not sufficient. The coupling itself, how quantities are passed across the interface and how the coupled iteration converges, introduces new errors that neither code exhibits alone. The coupled system needs its own verification.
Sources of Coupling Error
- Interpolation error, when data is mapped between meshes that do not match at the interface.
- Interface consistency error, when conservation is not preserved across the boundary between codes.
- Coupling iteration error, when the back-and-forth between codes is stopped before it converges.
- Time-integration error, from the scheme used to advance the coupled system in time.
Verifying the Coupling
The manufactured-solution method extends to coupled systems: choose exact solutions for each physics that are consistent at the interface, derive the sources each code needs, and confirm the coupled system reproduces them at the expected order. This tests the data transfer and the coupling scheme, not just the individual solvers. Conservation across the interface is a natural additional check, since a well-coupled system should not create or destroy conserved quantities at the boundary.
Coupling Convergence
When codes exchange data and iterate to a consistent state, that iteration has its own convergence error, analogous to iterative error in a single solver. Stopping it too early leaves the two physics inconsistent, an error that varies with the case and can corrupt a convergence study of the coupled system. The coupling tolerance must be tight enough that this inconsistency is negligible relative to the discretization error being studied.
The lesson mirrors the whole field: separately verified pieces do not guarantee a verified whole. The interfaces and the coupling scheme are code too, and they demand the same order-of-accuracy and conservation scrutiny as the solvers they connect.