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Computing residual diffusivity by adaptive basis learning via spectral method

Jiancheng Lyu Jack Xin Yifeng Yu

Analysis of PDEs mathscidoc:1912.43887

Numerical Mathematics: Theory, Methods and Applications, 10, (2), 351-372, 2017.5
We study the residual diffusion phenomenon in chaotic advection computationally via adaptive orthogonal basis. The chaotic advection is generated by a class of time periodic cellular flows arising in modeling transition to turbulence in Rayleigh-Bnard experiments. The residual diffusion refers to the non-zero effective (homogenized) diffusion in the limit of zero molecular diffusion as a result of chaotic mixing of the streamlines. In this limit, the solutions of the advection-diffusion equation develop sharp gradients, and demand a large number of Fourier modes to resolve, rendering computation expensive. We construct adaptive orthogonal basis (training) with built-in sharp gradient structures from fully resolved spectral solutions at few sampled molecular diffusivities. This is done by taking snapshots of solutions in time, and performing singular value decomposition of the matrix consisting of these
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@inproceedings{jiancheng2017computing,
  title={Computing residual diffusivity by adaptive basis learning via spectral method},
  author={Jiancheng Lyu, Jack Xin, and Yifeng Yu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210443495104451},
  booktitle={Numerical Mathematics: Theory, Methods and Applications},
  volume={10},
  number={2},
  pages={351-372},
  year={2017},
}
Jiancheng Lyu, Jack Xin, and Yifeng Yu. Computing residual diffusivity by adaptive basis learning via spectral method. 2017. Vol. 10. In Numerical Mathematics: Theory, Methods and Applications. pp.351-372. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210443495104451.
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