Exponential time differencing for the tracer equations appearing in primitive equation ocean models

Calandrini, Sara; Pieper, Konstantin; Gunzburger, Max D.

doi:10.1016/j.cma.2020.113002

Exponential time differencing for the tracer equations appearing in primitive equation ocean models

Journal Article · Mon Jun 15 00:00:00 EDT 2020 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2020.113002· OSTI ID:1657893

Calandrini, Sara ^[1]; ^[2]; Gunzburger, Max D. ^[1]

Florida State Univ., Tallahassee, FL (United States)
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

The tracer equations are part of the primitive equations used in ocean modeling and describe the transport of tracers, such as temperature, salinity or chemicals, in the ocean. Depending on the number of tracers considered, several equations may be added to and coupled to the dynamics system. In many relevant situations, the time-step requirements of explicit methods imposed by the transport and mixing in the vertical direction are more restrictive than those for the horizontal, and this may cause the need to use very small time steps if a fully explicit method is employed. To overcome this issue, we propose an exponential time differencing (ETD) solver where the vertical terms (transport and diffusion) are treated with a matrix exponential, whereas the horizontal terms are dealt with in an explicit way. In this work, we investigate numerically the computational speed-ups that can be obtained over other semi-implicit methods, and we analyze the advantages of the method in the case of multiple tracers.

View Accepted Manuscript (DOE)

Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC)

Grant/Contract Number:: AC05-00OR22725; SC0016591

OSTI ID:: 1657893

Alternate ID(s):: OSTI ID: 1608173

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Journal Issue: . Vol. 365; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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