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

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 FZβ 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.

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