Mathmatic Abstraction for Fluid-structure Interaction Analysis of Bioprosthetic Heart Valves with Immersed Boundary Method
Abstract
Mathmatic abstraction, exactly variational formulations, is considered a fundamental work in engineering analysis. Fluid-structure interaction (FSI) is a field with no analytical solution, need increasingly use of numerical solutions. Designers and analysts devoted to this issue had paved a large path toward utilization of immersed boundary (IB) method. The study begines with mechanical modeling of involving materials. Due to the distinct mechanical response of aortic valves and its surrounding blood, normal numerical technique cannot achieve an approximation for precise hemodynamics analysis. In this paper, we introduced physically exact models for both fluid and solid, which are incompressible viscous Newton fluid and hyperelastic nonlinear anisotropic solid. we described the valves in a Lagrangian expression and used Eulerian coordinate for bloodstream. Then we set up the boundary conditions on the interfaces of both domains. Further, we applied IB method to avoid difficulties relating the two kinds of models by giving a reasonable term of force to approximate data transformation across the boundary. Finally, we gain several PDEs that govern the whole FSI system with specific initials.
Keywords
Mathmatic abstraction; Bioprosthetic heart valves; Fluid-structure interaction; Immersed boundary method
DOI
10.12783/dtetr/mcemic2016/9536
10.12783/dtetr/mcemic2016/9536
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