Numerical simulation and mathematical analysis of flow-wall interaction in the large deformation application to the dynamics of the aneurysms

Year 2015, , 42 - 60, 01.01.2015

Hamadiche Mahmoud

https://doi.org/10.18186/jte.03138

Cited By: 1

Abstract

Keywords

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Numerical simulation and mathematical analysis of flow-wall interaction in the large deformation application to the dynamics of the aneurysms

Abstract

A numerical method is derived to take account of full flowwall interaction in la large deformation domain. To this end, a simplified Lagrangian and nonlinear model is derived to describe the wall motion. the flow is described by two dimensional Naiver stokes equation. The projection method is used to solve for the flow and fourth Rung-Kutta method is used to solve wall equation. The formulation of the problem allows full flow and wall interaction via the boundary conditions at the interface flow-wall. Some numerical simulation will be presented with periodic inlet flow. The method is applied to study the dynamics of aneurysms in arteries and veins. The flow inside the aneurysm is examined under the effects of a steady inlet flow as well as a pulsatile inlet flow for different aneurysm sizes. The wall model is analyzed when the wall is subjected to a constant transmural pressure and a quasi uniform inviscid flow. For a steady constant transmural pressure, a formal solution of the non linear integral-partial differential equation governing the wall motion is derived. For a steady and a quasi uniform inviscid flow, a first integral of the wall equation is obtained, then the solution is found to satisfy an integral non linear equation which is solved by numerical iteration

Keywords

Numerical simulation, flow-wall interaction, large deformation

References

• Lasheras, J. C. 2010 Haemodynamic stresses and the onset
• and progression of vascular diseases. J. Fluid Mech. 664, 1-4.
• Lasheras, J. C. 2007 The biomechanics of arterial aneurysms. Annu. Rev. Fluid Mech. 39, 293-319.
• Duclaux, V., Gallaire, F. & Clanet, Ch. 2010 A fluid mechanical view on abdominal aortic aneurysms. J. Fluid Mech. 664, 5-32.
• Hamadiche, M., Scot, J. & Jeandel, D. 1994 Temporal stability of Jeffery-Hamel flow. J. Fluid Mech. 268, 71- 88.
• Fung, Y. C. 1990 Biomechanics. Motion, Flow, Stress and Growth. Springer-Verlag, New York.
• Humphrey, J. D. 1995 Mechanics of the Arterial Wall: Review and Directions. Crit. Rev. Biomed. Eng. 23, 1- 162.
• Holzapfel, G. A., Gasser, Th. C. & Ogden, R. W. 2004 Comparison of a Multi-Layer Structural Model for Arterial Walls With a Fung-Type Model, and Issues of Material Stability. Transactions ASME. 126(4), 264-275.
• Sheidaei, A., Hunley, S. C., Zeinali-Davarani, S., Raguin, L. G. & Baek S. 2011 Simulation of abdominal aortic aneurysm growth with updating hemodynamic loads using a realistic geometry. medical Engineering & physics. 33, 80-90.
• Figueroa, C. A., Baek, S., Taylor, C. A. & Humphrey J. D. 2009 A computational framework for fluid-solid-growth modeling in cardiovascular simulations. Computer Methods in Applied Mechanics and Engineering. 198 3583-3602.
• Bertram, C. D. & Castles, R. J. 1999 Flow limitation in uniform thick-walled collapsible tubes. International Journal of Solids and Structures. 13, 399-418.
• Duvaut, G. 1998 Mécanique des milieux continus. Dunod, Paris.
• Hamadiche, M., Kizilova, N. & Gad-el-Hak, M. 2009 Suppression of Absolute Instabilities in the Flow Inside a Compliant Tube. Communications in Numerical Methods in Engineering. 25, 505-531.
• Hamadiche, M. & Gad-el-Hak, M. 2004 Spatiotemporal Stability of Flow through Collapsible, viscoelastic tubes. AIAA journal. 42, No. 4, 772-786.
• Hamadiche, M. & Gad-el-Hak, M. 2002 Temporal Stability of Flow through Viscoelastic Tubes. Journal of Fluids and Structures. 16, No 3, 331-359.
• Olivier Doaré and E ; de Langre The flow-induced instability of long hanging pipes,Europen Journal of Mechanics A/Solide Volume 21, 2002, Pages 857-867
• Hamadiche, M. and Abu Shadi, H. 2006 Flow induced vibration during the optic fiber coating process. Journal Fluid and Structure, Vol. 22(5), p. 599-615.
• B. H. Tan, A.D. Lucey and R. M. Howell Aero-/hydro- elastic stability of flexible panels: Prediction and control using localised spring support, Journal of Sound and Vibration Volume 332, Issue 26, 23 December 2013, Pages 7033-7054
• Whittaker, J. R., Heil, M., Jensen, O. E. & Waters, W. L. 2010 Predicting the onset of high-frequency self-excited oscillations in elastic-walled tubes. Proc. R. Soc. 466, 3635-3657.