Reduced fluid-structure interaction models have received a considerable attention in recent years being the key component of hemodynamic modeling. A variety of models applying to specific physiological components such as arterial, venous and cerebrospinal fluid (CSF) circulatory systems have been developed based on different approaches. The purpose of this paper is to apply the general approach based on Hamilton’s variational principle to create a model for a viscous Newtonian fluid - structure interaction (FSI) in a compliant bifurcated network. This approach provides the background for a correct formulation of reduced FSI models with an account for arbitrary nonlinear visco-elastic properties of compliant boundaries. The correct boundary conditions are specified at junctions, including matching points in a combined 3D/1D approach. The hyperbolic properties of derived mathematical model are analyzed and used, constructing the monotone finite volume numerical scheme, second-order accuracy in time and space. The computational algorithm is validated by comparison of numerical solutions with the exact manufactured solutions for an isolated compliant segment and a bifurcated structure. The accuracy of applied TVD (total variation diminishing) and Lax-Wendroff methods are analyzed by comparison of numerical results to the available analytical smooth and discontinuous solutions.

Publication Date



Presented at the Proceedings of the 2nd World Congress on Momentum, Heat and Mass Transfer (MHMT’17), Barcelona, Spain, April 6-8, 2017

Document Type

Conference Paper

Department, Program, or Center

Mechanical Engineering (KGCOE)


RIT – Main Campus