YZβ discontinuity capturing for advection-dominated processes with application to arterial drug delivery

Y. Bazilevs*, V. M. Calo, T. E. Tezduyar, T. J.R. Hughes

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

129 Scopus citations


The YZβ discontinuity-capturing operator, recently introduced in (Encyclopedia of Computational Mechanics, Vol. 3, Fluids. Wiley: New York, 2004) in the context of compressible flows, is applied to a time-dependent, scalar advection-diffusion equation with the purpose of modelling drug delivery processes in blood vessels. The formulation is recast in a residual-based form, which reduces to the previously proposed formulation in the limit of zero diffusion and source term. The NURBS-based isogeometric analysis method, proposed by Hughes et al. (Comput. Methods Appl. Mech. Eng. 2005; 194:4135-4195), was used for the numerical tests. Effects of various parameters in the definition of the YZβ operator are examined on a model problem and the better performer is singled out. While for low-order B-spline functions discontinuity capturing is necessary to improve solution quality, we find that high-order, high-continuity B-spline discretizations produce sharp, nearly monotone layers without the aid of discontinuity capturing. Finally, we successfully apply the YZβ approach to the simulation of drug delivery in patient-specific coronary arteries.

Original languageEnglish (US)
Pages (from-to)593-608
Number of pages16
Issue number6-8
StatePublished - Jul 20 2007
Externally publishedYes


  • Advection-diffusion equation
  • Discontinuity capturing
  • Drug delivery
  • Fluids
  • Interior layers
  • Isogeometric analysis
  • Navier-Stokes equations

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics
  • Computer Science Applications
  • Computational Mechanics


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