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Stability Analysis of Coupled Advection-Diffusion Models with Bulk Interface Condition

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Abstract

Numerical stability is of critical importance in general circulation models because it affects the design of algorithms, time to solution, and computational costs associated with the simulations, which are very expensive in practice. In this paper we extend the stability analysis for ocean-atmosphere coupling proposed in [Zhang et al., J. Sci. Comput. 84, 44(2020)] to a more realistic model that includes horizontal advection. We analyze various time-stepping strategies. We find that advection has a stabilizing effect in scenarios common to climate models when bulk interface condition and explicit flux coupling are used. We also show that our method can be used to study the stability impact of advection for other interface conditions such as Dirichlet–Neumann conditions.

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Data Availability

Data sharing not applicable to this article as no datasets were generated or analysed during the current study.

Abbreviations

T :

Temperature variable

x :

Horizontal spatial variable

z :

Vertical spatial variable

\(\Delta z\) :

Grid size in z direction

t :

Time variable

\(\Delta t\) :

Time step size

K :

Large-eddy diffusion coefficient

\(\nu \) :

Dynamic diffusivity

U :

Large-eddy advection velocity

u :

Advection velocity

\(\rho \) :

Density

c :

Heat capacity

\({\hat{\alpha }}\) :

Bulk coefficient

b :

Derived variable, \(b=\rho c {\hat{\alpha }}\)

k :

Wave number for Fourier transform

f :

Diffusion flux

h :

Interfacial flux

\(\beta \) :

Bulk Courant number

d :

Diffusion Counrant number

\({\mathcal {A}}\) :

Amplification factor

\(\kappa \) :

A function of space

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Funding

This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research and Office of Biological and Environmental Research, Scientific Discovery through Advanced Computing (SciDAC) program under contract number DE-AC02-06CH11357.

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Authors and Affiliations

  1. Mathematics and Computer Science Division, Argonne National Laboratory, Lemont, 60439, IL, US

    Hong Zhang, Emil Constantinescu & Robert Jacob

  2. Department of Geography, Ohio State University, Columbus, 43210, OH, US

    Zhengyu Liu

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All authors contributed to the study conception and design. Analysis were performed by Hong Zhang and Zhengyu Liu. The first draft of the manuscript was written by Hong Zhang and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, under contract DE-AC02-06CH11357, and by the Office of Biological and Environmental Research, Scientific Discovery through Advanced Computing (SciDAC) program, through the Coupling Approaches for Next-Generation Architectures (CANGA) project.

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Zhang, H., Liu, Z., Constantinescu, E. et al. Stability Analysis of Coupled Advection-Diffusion Models with Bulk Interface Condition. J Sci Comput 93, 33 (2022). https://doi.org/10.1007/s10915-022-01983-9

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