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

Abstract

AbstractThe 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. Copyright © 2007 John Wiley & Sons, Ltd.