High-resolution multi-domain space–time isogeometric analysis of car and tire aerodynamics with road contact and tire deformation and rotation

Takashi Kuraishi, Zhaojing Xu, Kenji Takizawa*, Tayfun E. Tezduyar, Satoshi Yamasaki

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


We are presenting high-resolution space–time (ST) isogeometric analysis of car and tire aerodynamics with near-actual tire geometry, road contact, and tire deformation and rotation. The focus in the high-resolution computation is on the tire aerodynamics. The high resolution is not only in space but also in time. The influence of the aerodynamics of the car body comes, in the framework of the Multidomain Method (MDM), from the global computation with near-actual car body and tire geometries, carried out earlier with a reasonable mesh resolution. The high-resolution local computation, carried out for the left set of tires, takes place in a nested MDM sequence over three subdomains. The first subdomain contains the front tire. The second subdomain, with the inflow velocity from the first subdomain, is for the front-tire wake flow. The third subdomain, with the inflow velocity from the second subdomain, contains the rear tire. All other boundary conditions for the three subdomains are extracted from the global computation. The full computational framework is made of the ST Variational Multiscale (ST-VMS) method, ST Slip Interface (ST-SI) and ST Topology Change (ST-TC) methods, ST Isogeometric Analysis (ST-IGA), integrated combinations of these ST methods, element-based mesh relaxation (EBMR), methods for calculating the stabilization parameters and related element lengths targeting IGA discretization, Complex-Geometry IGA Mesh Generation (CGIMG) method, MDM, and the “ST-C” data compression. Except for the last three, these methods were used also in the global computation, and they are playing the same role in the local computation. The ST-TC, for example, as in the global computation, is making the ST moving-mesh computation possible even with contact between the tire and the road, thus enabling high-resolution flow representation near the tire. The CGIMG is making the IGA mesh generation for the complex geometries less arduous. The MDM is reducing the computational cost by focusing the high-resolution locally to where it is needed and also by breaking the local computation into its consecutive portions. The ST-C data compression is making the storage of the data from the global computation less burdensome. The car and tire aerodynamics computation we present shows the effectiveness of the high-resolution computational analysis framework we have built for this class of problems.

Original languageEnglish
Pages (from-to)1257-1279
Number of pages23
JournalComputational Mechanics
Issue number6
Publication statusPublished - 2022 Dec


  • Car and tire aerodynamics
  • High-resolution computational analysis
  • Multidomain method
  • Road contact
  • ST Isogeometric Analysis (ST-IGA)
  • ST Slip Interface (ST-SI) method
  • ST Topology Change (ST-TC) method
  • ST Variational Multiscale (ST-VMS) method

ASJC Scopus subject areas

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


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