The paper asks whether AC/DC can make global non-hydrostatic ocean modelling affordable while representing a wider range of motions. Its operation-count analysis puts AC/DC at about 10 passes through the model per step, including 1.78 passes of overhead. Relative to a hydrostatic step, the quoted cost ratio ranges from 1.21 to 1.27, or about 1.22.
That is a work estimate, not a measured runtime. Under the stated configuration, the paper estimates wall-clock time at about 1.3 to 1.4 times hydrostatic time, with an upper bound near 1.45. The manuscript labels the figure a scale estimate, not a measurement or a theorem.
A local route through pressure
AC/DC organizes pressure work locally. It combines a vertical tridiagonal pressure solve within each column with horizontal artificial-compressibility relaxation, a numerical pressure-adjustment step. The horizontal work uses nearest-neighbour communication, and the pressure calculation has no global stop of its own.
The numerical section reports six experiments, with four described as genuinely non-hydrostatic physical tests. The named cases include E1, a lock-exchange gravity current, E2, internal gravity-wave dispersion, and E3, open-ocean deep convection. AC/DC values are generally reported against a projection reference run on the same mesh and time step.
The conservation analysis says flux-form pseudo-density transport and density weighting support identically conserved density-weighted energy, conserved tracer content with a uniformly bounded representation error, and a discrete tracer-variance identity.
Results that held up against the reference
In a stated grid-scale comparison, relative divergence was approximately 10−6 for pure three-dimensional artificial compressibility and 10−10 for AC/DC. The paper treats this as a configuration-specific result, and finite-parameter AC/DC still retains residual divergence rather than exact incompressibility.
The lock-exchange case produced close front-speed agreement with projection. Differences in the front-Froude result were 2.2 × 10−4 and 1.8 × 10−4 on the listed resolutions, while changing the mesh shifted the result by 2.1 × 10−2. In this test, the mesh effect was larger than either algorithm difference.
The same case also reported tight tracer and pseudo-mass checks. Tracer content differed from projection by 1 × 10−15, while the reported AC/DC difference was zero. Agreement between pseudo-mass and the flux-form balance was 1.2 × 10−10.
Mixing showed why close method agreement does not remove resolution effects. At model time 8, numerical mixing divided by configured diffusivity was 12.14 for projection and 12.06 for AC/DC on the coarser mesh. On the finer mesh, the ratio was 3.40 for both methods, so numerical mixing still exceeded the configured diffusivity but was much lower.
An internal gravity-wave test gave small analytical dispersion errors at the development resolution and the stated setting of 1. For nx equal to 1, 2, 4 and 8, the AC/DC errors were 4.1 × 10−5, 2.6 × 10−5, 9.0 × 10−6 and 2.5 × 10−6. The reported values matched the formula associated with the paper's proposition to all reported digits.
Deep convection sets the boundary
Deep convection was the clearest stress test. The three lower tested values of alpha, the artificial-compressibility parameter, became unstable and produced NaNs by model time about 0.012 to 0.015. The largest tested alpha completed and tracked projection: plume depth was 0.8 for both methods, while maximum vertical speeds were 1963 for projection and 2105 for AC/DC.
Paired convection runs also followed the reported inverse-alpha pattern. The observed error ratios ranged from 8.94 to 9.01, against an exact expected ratio of 9. The paper reports this relationship in the stated configuration, so the result describes the tested runs rather than establishing a universal rule.
One direct timing comparison was less favorable to AC/DC than the scale estimate. Across 5,200 steps, the reported timings were 428.6 milliseconds for AC/DC and 327.2 milliseconds for projection, making projection 1.31 times faster. The comparison was non-global and state-dependent.
The result is a numerical case for a local-pressure route to non-hydrostatic ocean modelling, but the runtime figures remain estimates and the direct timing sample was non-global. The paper's central question is still whether the method can make global modelling affordable under production conditions.
The manuscript is an arXiv preprint, version 2, dated 28 August 2026. Its evidence comes from the stated numerical experiments, discrete analysis and cost accounting, providing a basis for further testing of the method.
Paper data and sources
Original title: A Computational Model for Global Ocean Dynamics at all Scales
Authors: Peter Korn
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text