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

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

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