A flux-interpolated advection scheme for fluid simulation

Abstract

We propose a new advection scheme for fluid simulation that improves both conservation and numerical diffusion. Our work differs from previous works in that we re-formulate interpolation as cell-face flux of a vector field instantly constructed from a scalar field, rather than a per-point evaluation at back-traced positions. Our novel interpolation method enables excellent preservation of conservative quantities since the sum of flux exactly counteracts on cell faces, which eventually evaluates the boundary-flux of the whole domain. Our method can be implemented as a plug-and-play extension (or a temporary scratchpad) to the conventional semi-Lagrangian scheme; hence, our method naturally inherits all the benefits of semi-Lagrangian schemes and can be seamlessly integrated with existing fluid simulation pipelines together with other (black-boxed) solver components. We conducted numerical experiments to verify the accuracy of our scheme (conservation and the improved numerical diffusion) and compared its qualitative results with state-of-the-art advection schemes that are in heavy use in the production environment such as MacCormack and the WENO6 interpolation.

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Acknowledgements

This study is supported by JSPS Grant-in-Aid for Young Scientists (18K18060).

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Correspondence to Naoyuki Hirasawa.

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Hirasawa, N., Kanai, T. & Ando, R. A flux-interpolated advection scheme for fluid simulation. Vis Comput (2021). https://doi.org/10.1007/s00371-021-02187-2

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Keywords

  • Computer graphics
  • Fluid simulation
  • Conservative advection
  • Predictive diffusion correction
  • Flux interpolation