Scalar auxiliary variable approache for the surface quasi-geostrophic equation

We present a numerical method for approximating the two-dimensional surface quasi-geostrophic equation. We first reformulate the equation into an equivalent system by using the scalar auxiliary variable approach. Then we propose first-order and second-order discretization schemes for solving the new...

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Bibliographic Details
Published inJournal of algorithms & computational technology Vol. 17
Main Authors Shi, Shengtao, Song, Fangying
Format Journal Article
LanguageEnglish
Published London, England SAGE Publications 01.06.2023
Sage Publications Ltd
SAGE Publishing
Subjects
Linear equations
Numerical methods
Scalar auxiliary variable
fractional reaction-diffusion equation
unconditionally stable
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Summary:We present a numerical method for approximating the two-dimensional surface quasi-geostrophic equation. We first reformulate the equation into an equivalent system by using the scalar auxiliary variable approach. Then we propose first-order and second-order discretization schemes for solving the new surface quasi-geostrophic system in time. Furthermore, we prove that both of these schemes based on the scalar auxiliary variable approach satisfy an unconditionally energy stability property. Since the method gives two linear equations with constant coefficients in each time step. We have an efficient approach and accurate for solving these spacial fractional diffusion equations. Ample numerical experiments are carried out to validate the correctness of these schemes and their accuracy for inviscid problems and the problems with small viscosity.
ISSN:1748-3018
1748-3026
DOI:10.1177/17483026231176203