First-order system least-squares (FOSLS) for modeling blood flow

References 

1. Brandt A. Multi-level adaptive solutions to boundary value problems. Math Comput. 1977;31:333–390
2. Cai Z, Manteuffel T, McCormick S. First-order system least squares for the Stokes equations, with application to linear elasticity. SIAM J Numer Anal. 1997;34(5):1727–1741
3. Cai Z, Mantueffel T, McCormick S. First-order system least squares for second-order partial differential equations, Part ii. SIAM J Numer Anal. 1997;34(2):425–545
4. Codd A, Manteuffel T, McCormick S, Ruge JW. Multilevel first-order system least squares for elliptic grid generation. SIAM J Numer Anal. 2003;41(6):2210–2232
5. DeGroff C, Orlando W, Shandas R. Insights into the effect of aortic compliance on Doppler diastolic flow patterns seen in coarctation of the aorta: a numerical study. J Am Soc Echocardiogr. 2003;16:162–169
   • Abstract
   • Full Text
   • Full-Text PDF (248 KB)
   • CrossRef
6. Ghattas O, Li X. A variational finite element method for stationary nonlinear fluid–solid interaction. J Comput Phys. 1995;121:347–356
7. Heil M. Stokes flow in an elastic tube—a large-displacement fluid–structure interaction problem. Int J Numer Meth Fluids. 1998;28:243–265
8. Heys J, Manteuffel T, McCormick S, Ruge J. First-order systems least squares (FOSLS) for coupled fluid–elastic problems. J Comput Phys. 2004;195(2):560–575
9. Knupp P, Steinberg S. Fundamentals of grid generation. Boca Raton, FL: CRC Press; 1993;
10. Ku D. Blood flow in arteries. Annu Rev Fluid Mech. 1997;29:399–434
11. Lai M-C, Peskin C. An immersed boundary method with formal second-order accuracy and reduced numerical viscosity. J Comput Phys. 2000;160:705–719
12. Lee L, LeVeque R. An immersed interface method for incompressible Navier–Stokes equations. SIAM J Sci Comput. 2003;25:832–856
13. Perktold K, Rappitsch G. Mathematical modeling of local arterial flow and vessel mechanics. In:  Crolet J,  Ohayon R editor. Computational methods for fluid–structure interaction, vol. 306: Pitman research notes in mathematics series. New York: Longman Scientific and Technical/Wiley; 1994;p. 230–245
14. Perktold K, Rappitsch G. Computer simulation of local blood flow and vessel mechanics in a compliant carotid artery bifurcation model. J Biomech. 1995;28(7):845–856
    • Abstract
    • Full-Text PDF (2084 KB)
    • CrossRef
15. Perktold K, Thurner E, Kenner T. Flow and stress characteristics in rigid walled and compliant carotid artery bifurcation models. Med Biol Eng Comput. 1994;32:19–26
    • MEDLINE
16. Peskin C. Numerical analysis of blood flow in the heart. J Comput Phys. 1977;25:220–252
17. Rast M. Simultaneous solution of the Navier–Stokes and elastic membrane equations by a finite element method. Int J Numer Meth Fluids. 1994;19:1115–1135
18. Ruge J, Stüben K. Algebraic multigrid. In:  McCormick SF editors. Multigrid methods, vol. 3: Frontiers in applied mathematics. Philadelphia: SIAM; 1987;p. 73–130
19. Shahcheraghi N, Dwyer H, Cheer A, Barakat A, Rutaganira T. Unsteady and three-dimensional simulation of blood flow in the human aortic arch. J Biomech Eng. 2002;124:378–387
    • MEDLINE
    • CrossRef
20. Tang D, Anderson D, Biz S, Ku D. Steady viscous flow in constricted elastic tubes subjected to a uniform external pressure. Int J Numer Meth Eng. 1998;41:1391–1415
21. Tu C, Peskin C. Stability and instability in the computation of flows with moving immersed boundaries: a comparison of three methods. SIAM J Sci Statist Comput. 1992;13(6):1361–1376