Xi-Yuan (Bruce) Yin

I'm a postdoctoral researcher at the Fluid Mechanics and Acoustics Laboratory at l'École centrale de Lyon where I work in the Turbulence and Instabilities team under the mentorship of Prof. Wouter Bos within the ANR project CM2E.

I obtained my PhD in Mathematics at McGill University in 2021 under the supervision of Prof. Jean-Christophe Nave. During my thesis, I mainly worked on the characteristic mapping method for the incompressible Euler equations in two and three dimensions.

Research Interests

Most of my work so far is centered around the study of numerical methods for advection dominated problems. While computational fluid mechanics is the principal focus of my reseach, I also have a strong interest for the relevant underlying mathematical theories:

• Numerical analysis
• Analysis of partial differential equations
• Differential geometry (in particular, Geometric Hydrodynamics)

My current research is focused on employing the characteristic mapping method to help the physical understanding of turbulent flows and to explore the novel perspectives the geometric approach could bring.

Publications

• X.-Y. Yin, W. Agoua, T. Wu, W. Bos, The influence of the vorticity-scalar correlation on mixing, (2024) preprint
  [arXiv:2402.16762]
• S. Taylor, X.-Y. Yin, J.-C. Nave, Functional discretization of the co-adjoint action on the diffeomorphism group for Euler-Poincare equations, (2023)
  in preparation
• W. Agoua, X.-Y. Yin, T. Wu, W. Bos, Coexistence and persistence of two equilibrium configurations in 2d truncated Euler equations, (2023)
  in preparation
• P. Krah, X.-Y. Yin, J. Bergmann, J.-C. Nave, K. Schneider, A characteristic mapping method for Vlasov-Poisson with extreme resolution properties, (2023) preprint
  [arXiv:2311.09379]
• J. Bergmann, T. Maurel-Oujia, X.-Y. Yin, J.-C. Nave, K. Schneider, Singularity formation of vortex sheets in 2d Euler equations using the characteristic mapping method, (2023)
  in preparation
• X.-Y. Yin, K. Schneider, J.-C. Nave, A Characteristic Mapping Method for the three-dimensional incompressible Euler equations, (2023) J. Comp. Phys. Volume 477, 111876
  [arXiv:2107.03504]
• X.-Y. Yin, O. Mercier, B. Yadav, K. Schneider, J.-C. Nave, A Characteristic Mapping Method for the two-dimensional incompressible Euler equations, (2021) J. Comp. Phys. Volume 424, 109781
  [arXiv:1910.10841]
• X.-Y. Yin, L. Chen, J.-C. Nave, A Diffusion-Driven Characteristic Mapping Method for Particle Management, (2021) SIAM J. Sci. Comp. Volume 43(5), A3155–A3183
  [arXiv:2008.13076]
• O. Mercier, X.-Y. Yin, J.-C. Nave, The Characteristic Mapping Method for the linear advection of arbitrary sets, (2020) SIAM J. Sci. Comp. Volume 42(3), A1663-A1685
  [arXiv:1309.2731]
• I. Balázs, J.B. van den Berg, J. Courtois, J. Dudás, J.P. Lessard, A. Vörös-Kiss, JF Williams, X.-Y. Yin, Computer-assisted proofs for radially symmetric solutions of PDEs, (2020) J. Comp. Dyn. Volume 5, 61-80
  [pdf]

Presentations and Conferences

• Coexistence of Different Equilibria in 2D Galerkin Truncated Euler Equations
  Réunion du GdR Navier-Stokes 2.00
  Université de Rouen Normandies, October 2023
• Kelvin-Filtered Turbulence and Relation to Space Locality
  18th European Turbulence Conference
  Universidad Politécnica de Valencia, September 2023
• Numerical study of high-Reynolds problems using the characteristic mapping method
  Séminaires du LMFA
  École Centrale de Lyon, May 2023
• Characteristic Mapping method and applications to the singularity problem in the 3D Euler equations
  Réunion du GdR Navier-Stokes 2.00
  École Centrale de Lille, November 2022