The study puts the estimated runtime of its AC/DC method at about 1.36 times a hydrostatic step and asks whether that added cost can support non-hydrostatic, convection-resolving scales in global ocean models. AC/DC is an artificial-compressibility approach that splits the thin-fluid pressure problem into a cheap local vertical component and a horizontal component handled without a global pressure solve.
The stated runtime range was 1.24 to 1.38 under the central efficiency assumption. The paper describes that figure as a scale estimate in a memory-bound regime, not a wall-clock measurement of AC/DC and not a theorem.
Matched tests
To test the solver itself, the study used a projection-method reference that solves the same discrete equations at every step. In direct comparisons, both methods used identical meshes, initial conditions, transport scheme and time integrator; only the velocity-update block changed.
In a lock-exchange benchmark, the two methods agreed on the front Froude number to 1.5 × 10−4 and 1.2 × 10−4. Changing the mesh moved the same measure by 1.5 × 10−2, a much larger shift. On the finer mesh at time 8, the viscous-dissipation mixing-efficiency estimate was 0.1878 for projection and 0.1879 for AC/DC. When total dissipation was used instead, the figures were 0.1830 and 0.1836, with corresponding reported Rf values of 0.1547 and 0.1551.
The wave tests reached a similar result. In the internal-gravity-wave operator test, the AC/DC dispersion result matched the analytical formula to all reported digits across four modes. In a standing free-surface wave experiment, six modes were tested across a reported range from 0.031 to 1.005. Period errors against the exact relation stayed within 1.24% for projection and 1.05% for AC/DC. Against the hydrostatic relation, the maximum reported errors were 16.15% and 15.93%, respectively.
The deep-convection test agreed on plume depth and minimum temperature anomaly, but its mixing comparison was less complete. At time 0.04, both solvers produced a plume depth of 0.8 and a minimum temperature anomaly of −1.00. Maximum vertical velocity was 1963 for the projection method and 2105 for AC/DC. In the projection run, the cumulative flux Richardson number was 0.718, with a reported mixing-efficiency coefficient of 2.55. The corrected AC/DC mixing value was reported only as an upper bound because pressure work and numerical dissipation were not separated.
Where the evidence stops
The method was also tested on a telescoping mesh whose cell areas spanned a factor of 79. AC/DC used no global operation and reproduced the projection solution’s main rise, head, return flow and mixing to within a few percent, with remaining differences confined to individual-cell scales.
Alongside the benchmarks, the theoretical analysis reports bounded, non-accumulating volume error, conservation of energy and tracer content, and preservation of non-hydrostatic internal-wave dispersion under the AC/DC approximation. The numerical tests are confined to idealized configurations and do not demonstrate large-scale high-resolution ocean experiments.
The runtime estimate depends on the stated configuration and memory-bound regime, while the artificial-compressibility calibration in the deep-convection experiment was experiment-specific. The evidence therefore describes a computational proposal tested in controlled cases; it does not demonstrate a large-scale high-resolution ocean experiment.
The supplied front matter identifies the work as an arXiv preprint, version 3, dated 5 September 2026. No funding statement is reported in the supplied text.
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