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\(YZ\beta\) discontinuity capturing for advection-dominated processes with application to arterial drug delivery. (English) Zbl 1207.76049

Summary: The \(YZ\beta\) discontinuity-capturing operator, recently introduced in [Stein, Erwin (ed.) et al., Encyclopedia of Computational Mechanics, Vol. 3, Fluids. Wiley: New York (2004; Zbl 1190.76001)] 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 T. J. R. Hughes et al. [Comput. Methods Appl. Mech. Eng. 194, No. 39–41, 4135–4195 (2005; Zbl 1151.74419)], was used for the numerical tests. Effects of various parameters in the definition of the \(YZ\beta\) 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 \(YZ\beta\) approach to the simulation of drug delivery in patient-specific coronary arteries.

MSC:

76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76Z05 Physiological flows
92C50 Medical applications (general)
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