Fractional spectral vanishing viscosity method: Application to the quasi-geostrophic equation

Fangying Song and George Em Karniadakis

Chaos, Solitons & Fractals, 2017, vol. 102, issue C, 327-332

Abstract: We introduce the concept of fractional spectral vanishing viscosity (fSVV) to solve conservations laws that govern the evolution of steep fronts. We apply this method to the two-dimensional surface quasi-geostrophic (SQG) equation. The classical solutions of the inviscid SQG equation can develop finite-time singularities. By applying the fSVV method, we are able to simulate these solutions with high accuracy and long-time integration with relatively low resolution. Numerical diffusion in fSVV can be tuned by the fractional order as needed. Hence, fSVV can also be applied to integer-order conservation laws that exhibit steep solutions and evolving fronts.

Keywords: Fractional conservations laws; Spectral element method; Singular solutions (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:102:y:2017:i:c:p:327-332

DOI: 10.1016/j.chaos.2017.03.052

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