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

International Journal for Numerical Methods in Fluids

Volumn 54, Issue 6-8, 2007, Pages 593-608

  Bazilevs, Y ^a   Calo, V M ^a   Tezduyar, T E ^b   Hughes, T J R ^a  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^b Rice University   (United States)

Author keywords

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

Indexed keywords

ADVECTION; BLOOD VESSELS; COMPRESSIBLE FLOW; COMPUTATIONAL GEOMETRY; COMPUTER SIMULATION; DIFFUSION; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; NAVIER STOKES EQUATIONS;

ADVECTION-DIFFUSION EQUATION; ARTERIAL DRUG DELIVERY; DISCONTINUITY-CAPTURING OPERATOR; ISOGEOMETRIC ANALYSIS;

DRUG DELIVERY;

ADVECTION; BLOOD VESSELS; COMPRESSIBLE FLOW; COMPUTATIONAL GEOMETRY; COMPUTER SIMULATION; DIFFUSION; DRUG DELIVERY; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; NAVIER STOKES EQUATIONS;

EID: 34347362891     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.1484     Document Type: Article

References (37)

1. Brooks AN, Hughes TJR. Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering 1982; 32:199-259.
2. Tezduyar TE. Finite element methods for fluid dynamics with moving boundaries and interfaces. In Encyclopedia of Computational Mechanics, Vol. 3: Fluids, Chapter 17, Stein E, De Borst R, Hughes TJR (eds). Wiley: New York, 2004.
3. Tezduyar TE, Senga M. Stabilization and shockcapturing parameters in SUPG formulation of compressible flows. Computer Methods in Applied Mechanics and Engineering 2006; 195:1621-1632.
4. Tezduyar TE, Senga M. SUPG finite element computation of inviscid supersonic flows with YZβ shock-capturing. Computers and Fluids 2007; 36:147-159.
5. Tezduyar TE, Senga M, Vicker D. Computation of inviscid supersonic flows around cylinders and spheres with the SUPG formulation and YZβ shock-capturing. Computational Mechanics 2006; 38:469-481.
6. Bazilevs Y, Beirao da Veiga L, Cottrell JA, Hughes TJR, Sangalli G. Isogeometric analysis: approximation, stability and error estimates for h-refined meshes. Mathematical Models and Methods in Applied Sciences 2006; 16:1031-1090.
7. Cottrell JA, Reali A, Bazilevs Y, Hughes TJR. Isogeometric analysis of structural vibrations. Computer Methods in Applied Mechanics and Engineering 2006; 195:5257-5297.
8. Hughes TJR, Cottrell JA, Bazilevs Y. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry, and mesh refinement. Computer Methods in Applied Mechanics and Engineering 2005; 194:4135-4195.
9. Chung J, Hulbert GM. A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-α method. Journal of Applied Mechanics 1993; 60:371-375.
10. Jansen KE, Whiting CH, Hulbert GM. A generalized-α method for integrating the filtered Navier-Stokes equations with a stabilized finite element method. Computer Methods in Applied Mechanics and Engineering 1999; 190: 305-319.
11. Zhang Y, Bazilevs Y, Goswami S, Bajaj C, Hughes TJR. Patient-specific vascular NURBS modeling for isogeometric analysis of blood flow. Computer Methods in Applied Mechanics and Engineering 2006, submitted for publication.
12. Akin JE, Tezduyar TE. Calculation of the advective limit of the SUPG stabilization parameter for linear and higher-order elements. Computer Methods in Applied Mechanics and Engineering 2004; 193:1909-1922.
13. Bischoff M, Bletzinger K-U. Improving stability and accuracy of Reissner-Mindlin plate finite elements via algebraic subgrid scale stabilization. Computer Methods in Applied Mechanics and Engineering 2004; 193: 1491-1516.
14. Bochev PB, Gunzburger MD, Shadid JN. On inf-sup stabilized finite element methods for transient problems. Computer Methods in Applied Mechanics and Engineering 2004; 193:1471-1489.
15. Burman E, Hansbo P. Edge stabilization for Galerkin approximations of convection-diffusion-reaction problems. Computer Methods in Applied Mechanics and Engineering 2004; 193:1437-1453.
16. Codina R, Soto O. Approximation of the incompressible Navier-Stokes equations using orthogonal subscale stabilization and pressure segregation on anisotropic finite element meshes. Computer Methods in Applied Mechanics and Engineering 2004; 193:1403-1419.
17. Coutinho ALGA, Diaz CM, Alvez JLD, Landau L, Loula AFD, Malta SMC, Castro RGS, Garcia ELM. Stabilized methods and post-processing techniques for miscible displacements. Computer Methods in Applied Mechanics and Engineering 2004; 193:1421-1436.
18. Gravemeier V, Wall WA, Ramm E. A three-level finite element method for the instationary incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering 2004; 193:1323-1366.
19. Harari I. Stability of semidiscrete formulations for parabolic problems at small time steps. Computer Methods in Applied Mechanics and Engineering 2004; 193:1491-1516.
20. Hauke G, Valiño L. Computing reactive flows with a field Monte Carlo formulation and multi-scale methods. Computer Methods in Applied Mechanics and Engineering 2004; 193:1455-1470.
21. Koobus B, Farhat C. A variational multiscale method for the large eddy simulation of compressible turbulent flows on unstructured meshes - application to vortex shedding. Computer Methods in Applied Mechanics and Engineering 2004; 193:1367-1383.
22. Masud A, Khurram RA. A multiscale/stabilized finite element method for the advection-diffusion equation. Computer Methods in Applied Mechanics and Engineering 2004; 193:1997-2018.
23. Tezduyar TE, Sathe S. Enhanced-discretization space-time technique (EDSTT). Computer Methods in Applied Mechanics and Engineering 2004; 193:1385-1401.
24. Tezduyar TE. Computation of moving boundaries and interfaces and stabilization parameters. International Journal for Numerical Methods in Fluids 2003; 43:555-575.
25. Tezduyar TE. Finite elements in fluids: stabilized formulations and moving boundaries and interfaces. Computers and Fluids 2007; 36:191-206.
26. Johnston BM, Johnston PR, Corney S, Kilpatrick D. Non-Newtonian blood flow in human right coronary arteries: transient simulation. Journal of Biomechanics 2006; 36:1116-1128.
27. Matsuo S, Tsuruta M, Hayano M, Immamura Y, Eguchi Y, Tokushima T, Tsuji S. Phasic coronary artery flow velocity determined by Doppler flowmeter catheter in aortic stenosis and aortic regurgitation. The American Journal of Cardiology 1988; 62:917-922.
28. Bazilevs Y, Calo VM, Zhang Y, Hughes TJR. Isogeometric fluid-structure interaction analysis with applications to arterial blood flow. Computational Mechanics 2006; 38:310-322.
29. Bazilevs Y. Isogeometric analysis of turbulence and fluid-structure interaction. Ph.D. Thesis, ICES, UT Austin, 2006.
30. Calo VM. Residual-based multiscale turbulence modeling: finite volume simulation of bypass transition. Ph.D. Thesis, Department of Civil and Environmental Engineering, Stanford University, Stanford, 2004.
31. Hughes TJR, Calo VM, Scovazzi G. Variational and multiscale methods in turbulence. In Proceedings of the XXI International Congress of Theoretical and Applied Mechanics (IUTAM), Gutkowski W, Kowalewski TA (eds). Kluwer: Dordrecht, 2004.
32. Holmen J, Hughes TJR, Oberai AA, Wells GN. Sensitivity of the scale partition for variational multiscale LES of channel flow. Physics of Fluids 2004; 16(3):824-827.
33. Hughes TJR, Mazzei L, Jansen KE. Large-eddy simulation and the variational multiscale method. Computing and Visualization in Science 2000; 3:47-59.
34. Hughes TJR, Mazzei L, Oberai AA, Wray AA. The multiscale formulation of large eddy simulation: decay of homogeneous isotropic turbulence. Physics of Fluids 2001; 13(2):505-512.
35. Hughes TJR, Oberai AA, Mazzei L. Large-eddy simulation of turbulent channel flows by the variational multiscale method. Physics of Fluids 2001; 13(6):1784-1799.
36. Hughes TJR, Scovazzi G, Franca LP. Multiscale and stabilized methods. In Encyclopedia of Computational Mechanics, Vol. 3, Computational Fluid Dynamics, Chapter 2, Stein E, De Borst R, Hughes TJR (eds). Wiley: New York, 2004.
37. Hughes TJR, Wells GN, Wray AA. Energy transfers and spectral eddy viscosity of homogeneous isotropic turbulence: comparison of dynamic Smagorinsky and multiscale models over a range of discretizations. Physics of Fluids 2004; 16:4044-4052.