OpenFOAM¶

This record compares solver-native FoamNordic functions with their standard OpenFOAM reference models. It isolates framework overhead and numerical parity; it does not assess the predictive quality of a learned closure.

Metrics¶

For a reference field \(\mathbf{r}\) and FoamNordic field \(\mathbf{f}\), the relative \(L_2\) error is

and the reported peak-relative error is

The scale floor \(s_{\min}\) is the smallest positive float for the pitzDaily comparisons and \(10^{-12}\) for NACA4412. Performance tables report the median and maximum absolute deviation defined in the benchmark reporting contract. Ratios use FoamNordic divided by the corresponding OF/FNO value; a ratio of \(1\) denotes equal elapsed time.

Validation matrix¶

pitzDaily nutFjord¶

Roihu compared OF/FNO with FNO-native nutFjord on the incompressible pitzDaily case using OpenFOAM v2512, 16 MPI ranks and deterministic simple (16 1 1) decomposition. Smagorinsky and WALE were each restarted from identical initial conditions and run independently for 1, 10, 100 and 400 steps with deltaT=1e-5.

Smagorinsky¶

The standard OpenFOAM Smagorinsky model used Ck=0.0265463553 and Ce=1.048; FNO-native evaluated the same float64 algebra through nutFjord without a ModelHost or field exchange.

Performance¶

Each path received one warm-up followed by seven measured 400-step runs in alternating order.

The end-to-end wall ratio was 1.074; the OpenFOAM execution-time ratio was 1.005. All seven measured pairs produced identical final fields.

Relative L2 error¶

Peak-relative error¶

WALE¶

The standard OpenFOAM WALE model used Cw=0.325; FNO-coupled evaluated the same float64 velocity-gradient invariant expression through nutFjord.

Performance¶

Each path received one warm-up followed by seven measured 400-step runs in alternating order.

The end-to-end wall ratio was 1.097; the OpenFOAM execution-time ratio was 1.034. All seven measured pairs produced identical final-field metrics.

Relative L2 error¶

Peak-relative error¶

The columns correspond to physical times 1e-5, 1e-4, 1e-3 and 4e-3. All values were finite and the direct float64 functions remained nonnegative. The runnable scripts are tools/hpc/benchmarkSmagorinskyInteractive.sh, tools/hpc/benchmarkWaleInteractive.sh and tools/hpc/validateNutClosure.sh.

NACA4412 kEqnFjord¶

k-equation configuration¶

Both NACA4412 paths ran on Roihu with 89,728 cells, OpenFOAM v2512, 16 MPI ranks, deltaT=0.0025 and 400 steps to physical time 1.

OF/FNO launched standard OpenFOAM kEqn through Longship. FNO-native used identical Ck=0.094 and Ce=1.048 algebra in Operator.function, with the implicit equation in Field.transport. The lowered kEqnFjord graph ran at the correction boundary without ModelHost or field exchange. Each path used one warm-up and seven measured runs, alternating execution order.

Performance¶

The end-to-end wall ratio was 1.079; the OpenFOAM execution-time ratio was 1.071. End-to-end wall includes Longship preparation, solver execution and shutdown.

Relative L2 error¶

Peak-relative error¶

The columns correspond to physical times 0.0025, 0.025, 0.25 and 1. Every measured pair produced the same final-field metrics and passed the declared relative L2 tolerance of 1e-2 and peak-relative tolerance of 5e-2. The runnable benchmark is tools/hpc/benchmarkNacaInteractive.sh.