A Finite Element Approach Derived From the Simplified Variational Principle

Author(s):  
Asher Yahalom

In previous papers [1–4] we have described how by minimizing the fluid action numerically one can obtain a solution of the fluid steady state equations. The action which was used was the four function action of Seliger & Whitham [5]. In a recent paper [6] we describe how one can improve upon previous art by reducing the number of variables in the action. Three independent functions variational formalism for stationary and non-stationary barotropic flows is introduced. This is less than the four variables which appear in the standard equations of fluid dynamics which are the velocity field ν⃗ and the density ρ. In this paper we will discuss a possible finite element approach related to the usage of the new action principles as basis for a CFD algorithms.

Stroke ◽  
2013 ◽  
Vol 44 (suppl_1) ◽  
Author(s):  
Haithem Babiker ◽  
L. Fernando Gonzalez ◽  
Brian Chong ◽  
David H Frakes

INTRODUCTION: Despite more than a decade of endovascular coil treatment, the effects of coils on cerebral aneurysm (CA) hemodynamics are still poorly understood. Coils present several challenges to in vivo and in vitro flow measurement techniques and previous in silico methods have suffered from large assumptions on coil geometry. Here we present the first fluid dynamic simulations of coiled CAs that consider the structure and deployment mechanics of embolic coils. We also investigate the influence of coil packing density, design, and configuration on CA fluid dynamics. Methods: Coil deployment was modeled using a novel finite element approach that realistically simulates coil dynamics during deployment. Two coil designs were investigated: helical and 3D. Coil design and material properties were matched to manufacturer specifications. Five deployment sequences of each coil design, at different microcatheter placements, were simulated in two idealized CA models with variable neck sizes. Blood flow was simulated using computational fluid dynamics. Simulated deployments and fluid dynamics were then compared to deployments of actual coils in identical physical CA models and in vitro particle image velocimetry flow measurements. Results: Simulated results closely matched in vitro data. Reductions in aneurysmal velocity magnitudes were largest for 3D coils and in a narrow-neck model. In that model, 3D coil deployments reduced average aneurysmal velocity magnitudes by a 51% - 69% range at packing densities less than 20% and by a 74% - 84% range at packing densities greater than 30%. Linear regression results showed reductions were strongly dependent on the spacing between coil loops within the aneurysm and packing density, with correlations of 0.6 and 0.7 respectively. Conclusion: Coil design and packing density may play equally important roles in determining CA hemodynamics. Results in an anatomical model will also be presented. The proposed virtual coiling approach represents a novel and effective method for realistically simulating coiled CAs, and is an important step towards clinical preoperative planning of coil treatment.


2007 ◽  
Vol 35 (3) ◽  
pp. 165-182 ◽  
Author(s):  
Maik Brinkmeier ◽  
Udo Nackenhorst ◽  
Heiner Volk

Abstract The sound radiating from rolling tires is the most important source of traffic noise in urban regions. In this contribution a detailed finite element approach for the dynamics of tire/road systems is presented with emphasis on rolling noise prediction. The analysis is split into sequential steps, namely, the nonlinear analysis of the stationary rolling problem within an arbitrary Lagrangian Eulerian framework, and a subsequent analysis of the transient dynamic response due to the excitation caused by road surface roughness. Here, a modal superposition approach is employed using complex eigenvalue analysis. Finally, the sound radiation analysis of the rolling tire/road system is performed.


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