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Analysis of Schwarz waveform relaxation for the coupled Ekman boundary layer problem with continuously variable coefficients
- Source :
- Numerical Algorithms, Numerical Algorithms, Springer Verlag, 2021, ⟨10.1007/s11075-021-01149-y⟩, Numerical Algorithms, 2022, 89, pp.1145-1181. ⟨10.1007/s11075-021-01149-y⟩
- Publication Year :
- 2021
- Publisher :
- Springer Science and Business Media LLC, 2021.
-
Abstract
- International audience; In this paper we present a global-in-time non-overlapping Schwarz method applied to the Ekman boundary layer problem. Such a coupled problem is representative of large-scale atmospheric and oceanic flows in the vicinity of the air-sea interface. Schwarz waveform relaxation (SWR) algorithms provide attractive methods for ensuring a "tight coupling" between the ocean and the atmosphere. However the convergence study of such algorithms in this context raises a number of challenges. Numerous convergence studies of Schwarz methods have been carried out in idealized settings, but the underlying assumptions to make these studies tractable may prohibit them to be directly extended to the complexity of climate models. We illustrate this aspect on the coupled Ekman problem, which includes several essential features inherent to climate modeling while being simple enough for analytical results to be derived. We investigate its well-posedness and derive an appropriate SWR algorithm. Sufficient conditions for ensuring its convergence for different viscosity profiles are then established. Finally, we illustrate the relevance of our theoretical analysis with numerical results and suggest ways to improve the computational cost of the coupling. Our study emphasizes the fact that the convergence properties can be highly sensitive to some model characteristics such as the geometry of the problem and the use of continuously variable viscosity coefficients.
- Subjects :
- coupled Ekman problem
010504 meteorology & atmospheric sciences
multiphysics coupling
Context (language use)
010103 numerical & computational mathematics
01 natural sciences
numerical climate modeling
Convergence (routing)
MESH: Schwarz waveform relaxation
Variable coefficients
Multiphysics coupling
Coupled Ekman problem
Numerical climate modeling
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
Waveform
Applied mathematics
0101 mathematics
Physics::Atmospheric and Oceanic Physics
0105 earth and related environmental sciences
Mathematics
[SDU.OCEAN]Sciences of the Universe [physics]/Ocean, Atmosphere
Applied Mathematics
Numerical analysis
continuously variable coefficients
Schwarz waveform relaxation
Boundary layer
Variable (computer science)
13. Climate action
Theory of computation
Relaxation (approximation)
[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Subjects
Details
- ISSN :
- 15729265 and 10171398
- Volume :
- 89
- Database :
- OpenAIRE
- Journal :
- Numerical Algorithms
- Accession number :
- edsair.doi.dedup.....dad9a45dd78bd59b8c148e139e8ed969