High Order Conservative Finite Difference/Fourier Spectral Methods for Inviscid Surface Quasi-Geostrophic Flows
Year: 2022
Author: Nan Zhang, Zhiping Mao, Tao Xiong
Communications in Computational Physics, Vol. 32 (2022), Iss. 5 : pp. 1474–1509
Abstract
In this paper, we develop an effective conservative high order finite difference scheme with a Fourier spectral method for solving the inviscid surface quasi-geostrophic equations, which include a spectral fractional Laplacian determining the vorticity for the transport velocity of the potential temperature. The fractional Laplacian is approximated by a Fourier-Galerkin spectral method, while the time evolution of the potential temperature is discretized by a high order conservative finite difference scheme. Weighted essentially non-oscillatory (WENO) reconstructions are also considered for comparison. Due to a low regularity of problems involving such a fractional Laplacian, especially in the critical or supercritical regime, directly applying the Fourier spectral method leads to a very oscillatory transport velocity associated with the gradient of the vorticity, e.g. around smooth extrema. Instead of using an artificial filter, we propose to reconstruct the velocity from the vorticity with central difference discretizations. Numerical results are performed to demonstrate the good performance of our proposed approach.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2022-0111
Communications in Computational Physics, Vol. 32 (2022), Iss. 5 : pp. 1474–1509
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 36
Keywords: Finite difference WENO Fourier spectral fractional Laplacian surface quasi-geostrophic flow.