Space-time VMS method for flow computations with slip interfaces (ST-SI)

Kenji Takizawa, Tayfun E. Tezduyar*, Hiroki Mochizuki, Hitoshi Hattori, Sen Mei, Linqi Pan, Kenneth Montel

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

98 Citations (Scopus)


We present the space-time variational multiscale (ST-VMS) method for flow computations with slip interfaces (ST-SI). The method is intended for fluid-structure interaction (FSI) analysis where one or more of the subdomains contain spinning structures, such as the rotor of a wind turbine, and the subdomains are covered by meshes that do not match at the interface and have slip between them. The mesh covering a subdomain with the spinning structure spins with it, thus maintaining the high-resolution representation of the boundary layers near the structure. The starting point in the development of the method is the version of the arbitrary Lagrangian-Eulerian VMS (ALE-VMS) method designed for computations with "sliding interfaces". Interface terms similar to those in the ALE-VMS version are added to the ST-VMS formulation to account for the compatibility conditions for the velocity and stress. In addition to having a high-resolution representation of the boundary layers, because the ST framework allows NURBS functions in temporal representation of the structure motion, we have exact representation of the circular paths associated with the spinning. The ST-SI method includes versions for cases where the SI is between fluid and solid domains with weakly-imposed Dirichlet conditions for the fluid and for cases where the SI is between a thin porous structure and the fluid on its two sides. Test computations with 2D and 3D models of a vertical-axis wind turbine show the effectiveness of the ST-SI method.

Original languageEnglish
Pages (from-to)2377-2406
Number of pages30
JournalMathematical Models and Methods in Applied Sciences
Issue number12
Publication statusPublished - 2015 Nov 26


  • Space-time VMS method
  • nonmatching meshes
  • slip interfaces
  • spinning structures
  • vertical-axis wind turbine
  • weakly-imposed Dirichlet conditions
  • zero-thickness structures with porosity

ASJC Scopus subject areas

  • Modelling and Simulation
  • Applied Mathematics


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