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

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  • Song, Fangying
  • Karniadakis, George Em

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.

Suggested Citation

  • Song, Fangying & Karniadakis, George Em, 2017. "Fractional spectral vanishing viscosity method: Application to the quasi-geostrophic equation," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 327-332.
    • Handle: RePEc:eee:chsofr:v:102:y:2017:i:c:p:327-332
    DOI: 10.1016/j.chaos.2017.03.052
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