Space–time computational analysis of tire aerodynamics with actual geometry, road contact, tire deformation, road roughness and fluid film

Takashi Kuraishi, Kenji Takizawa*, Tayfun E. Tezduyar

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

46 Citations (Scopus)


The space–time (ST) computational method “ST-SI-TC-IGA” has recently enabled computational analysis of tire aerodynamics with actual tire geometry, road contact and tire deformation. The core component of the ST-SI-TC-IGA is the ST Variational Multiscale (ST-VMS) method, and the other key components are the ST Slip Interface (ST-SI) and ST Topology Change (ST-TC) methods and the ST Isogeometric Analysis (ST-IGA). These ST methods played their parts in overcoming the computational challenges, including (i) the complexity of an actual tire geometry with longitudinal and transverse grooves, (ii) the spin of the tire, (iii) maintaining accurate representation of the boundary layers near the tire while being able to deal with the flow-domain topology change created by the road contact, and (iv) the turbulent nature of the flow. The combination of the ST-VMS, ST-SI and the ST-IGA has also recently enabled solution of fluid film problems with a computational cost comparable to that of the Reynolds-equation model for the comparable solution quality. This was accomplished with the computational flexibility to go beyond the limitations of the Reynolds-equation model. Here we include and address the computational challenges associated with the road roughness and the fluid film between the tire and the road. The new methods we add to accomplish that include a remedy for the trapped fluid, a method for reducing the number of control points as a space occupied by the fluid shrinks down to a narrow gap, and a method for representing the road roughness. We present computations for a 2D test problem with a straight channel, a simple 2D model of the tire, and a 3D model with actual tire geometry and road roughness. The computations show the effectiveness of our integrated set of ST methods targeting tire aerodynamics.

Original languageEnglish
Pages (from-to)1699-1718
Number of pages20
JournalComputational Mechanics
Issue number6
Publication statusPublished - 2019 Dec 1


  • Actual tire geometry
  • Fluid film
  • Road contact
  • Road roughness
  • ST Isogeometric Analysis (ST-IGA)
  • ST Slip Interface (ST-SI) method
  • ST Topology Change (ST-TC) method
  • ST Variational Multiscale (ST-VMS) method
  • Tire aerodynamics

ASJC Scopus subject areas

  • Computational Mechanics
  • Ocean Engineering
  • Mechanical Engineering
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics


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