Unsteady viscous flow model on moving the domain through a stenotic artery.

An unsteady Navier-Stokes (N-S) solver based on the method of operator splitting and artificial compressibility has been studied for the moving boundary problem to simulate blood flow through a compliant vessel. Galerkin finite element analysis is used to discretize the governing equations. The model has been applied to a time-varying computational domain (two-dimensional tube) as a test case for validation. Consideration has been given to retaining the space conservation property. The same code is then applied to a hypothetical critical high-pressure gradient over a short length of blood vessel based on the spring and dashpot model. The governing equation for the blood vessel is based on two-dimensional dynamic thin-shell theory that takes into account the curvature of the stenotic portion of the vessel. Progressing the solution towards steady state is considered, as the main objective is to show the viability of the current technique for fluid/structure interactions. Preliminary results of the wall velocity and displacement based on steady state prediction agree well with data in the literature. Results, such as the streamlines, wall pressures and wall shear stress depict the possible progression of arterial disease.