Stability constraints for oceanic numerical models: implications for the formulation of time and space discretizations
Stability constraints for oceanic numerical models: implications for the formulation of time and space discretizations
Except for vertical diffusion (and possibly the external mode and bottom drag), oceanic models usually rely on explicit time-stepping algorithms subject to Courant–Friedrichs–Lewy (CFL) stability criteria. Implicit methods could be unconditionally stable, but an algebraic system must be solved at each time step and other considerations such as accuracy and efficiency are less straightforward to achieve. Depending on the target application, the process limiting the maximum allowed time-step is generally different. In this paper, we introduce offline diagnostics to predict stability limits associated with internal gravity waves, advection, diffusion, and rotation. This suite of diagnostics is applied to a set of global, regional and coastal numerical simulations with several horizontal/vertical resolutions and different numerical models. We show that, for resolutions finer that 1/2°, models with an Eulerian vertical coordinate are generally constrained by vertical advection in a few hot spots and that numerics must be extremely robust to changes in Courant number. Based on those results, we review the stability and accuracy of existing numerical kernels in vogue in primitive equations oceanic models with a focus on advective processes and the dynamics of internal waves. We emphasize the additional value of studying the numerical kernel of oceanic models in the light of coupled space–time approaches instead of studying the time schemes independently from spatial discretizations. From this study, we suggest some guidelines for the development of temporal schemes in future generation multi-purpose oceanic models.
Space–time discretization schemes, Von-Neumann stability analysis, Advection schemes, Internal gravity waves
124-148
Lemarié, F.
a6651ef3-e385-4bb0-8f4a-4a4ab7310923
Debreu, L.
1019b20e-a5f4-4593-adc3-ad6f5c7de416
Madec, G.
7e2ec04b-896a-4861-b2d0-b74f39d748c2
Demange, J.
027acab8-8d03-43ff-a661-f58ef618a574
Molines, J.M.
d3ef07f2-dd14-433f-9ef2-d16a9f1a0d60
Honnorat, M.
6bf1bc60-17c5-40f8-aa68-478f175a145d
August 2015
Lemarié, F.
a6651ef3-e385-4bb0-8f4a-4a4ab7310923
Debreu, L.
1019b20e-a5f4-4593-adc3-ad6f5c7de416
Madec, G.
7e2ec04b-896a-4861-b2d0-b74f39d748c2
Demange, J.
027acab8-8d03-43ff-a661-f58ef618a574
Molines, J.M.
d3ef07f2-dd14-433f-9ef2-d16a9f1a0d60
Honnorat, M.
6bf1bc60-17c5-40f8-aa68-478f175a145d
Lemarié, F., Debreu, L., Madec, G., Demange, J., Molines, J.M. and Honnorat, M.
(2015)
Stability constraints for oceanic numerical models: implications for the formulation of time and space discretizations.
Ocean Modelling, 92, .
(doi:10.1016/j.ocemod.2015.06.006).
Abstract
Except for vertical diffusion (and possibly the external mode and bottom drag), oceanic models usually rely on explicit time-stepping algorithms subject to Courant–Friedrichs–Lewy (CFL) stability criteria. Implicit methods could be unconditionally stable, but an algebraic system must be solved at each time step and other considerations such as accuracy and efficiency are less straightforward to achieve. Depending on the target application, the process limiting the maximum allowed time-step is generally different. In this paper, we introduce offline diagnostics to predict stability limits associated with internal gravity waves, advection, diffusion, and rotation. This suite of diagnostics is applied to a set of global, regional and coastal numerical simulations with several horizontal/vertical resolutions and different numerical models. We show that, for resolutions finer that 1/2°, models with an Eulerian vertical coordinate are generally constrained by vertical advection in a few hot spots and that numerics must be extremely robust to changes in Courant number. Based on those results, we review the stability and accuracy of existing numerical kernels in vogue in primitive equations oceanic models with a focus on advective processes and the dynamics of internal waves. We emphasize the additional value of studying the numerical kernel of oceanic models in the light of coupled space–time approaches instead of studying the time schemes independently from spatial discretizations. From this study, we suggest some guidelines for the development of temporal schemes in future generation multi-purpose oceanic models.
This record has no associated files available for download.
More information
Published date: August 2015
Keywords:
Space–time discretization schemes, Von-Neumann stability analysis, Advection schemes, Internal gravity waves
Organisations:
Marine Systems Modelling
Identifiers
Local EPrints ID: 388131
URI: http://eprints.soton.ac.uk/id/eprint/388131
ISSN: 1463-5003
PURE UUID: 305b985a-4ee6-4cbb-a91e-a1ca983dd724
Catalogue record
Date deposited: 18 Feb 2016 14:37
Last modified: 14 Mar 2024 22:52
Export record
Altmetrics
Contributors
Author:
F. Lemarié
Author:
L. Debreu
Author:
G. Madec
Author:
J. Demange
Author:
J.M. Molines
Author:
M. Honnorat
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics