Rheological Models and Numerical Method for Simulation of Blood Flow

This paper describes a method and results of computational fluid dynamics (CFD) simulation of blood flow. Material properties of blood are assumed to be constant, homogeneous and isotropic. Blood is regarded as viscoplastic liquid, where two different rheological models are applied: Bingham and Casson model. Plastic viscosity and yield stress are given as a function of hematocrit. The flow regime is considered as laminar. Having applied rheological models to time dependent balance equations of mass and momentum conservation given in integral form, a finite-volume method is used for discretization. Discretization results in a set of systems of linearized algebraic equations which are solved individually, for blood velocity components and blood pressure, at every time step within a considered time interval. The method is applicable to domains of arbitrary shapes and unstructured computational meshes. The examples presented include: (a) pulsatile viscoplastic flow in a pipe representing a simplified blood vessel, where the solutions obtained with the two rheological models are compared to the numerical and analytical solution obtained with Newtonian liquid, as well as (b) blood flow in aorto-renal bifurcation and carotid artery branch. In analysis of the flow in the branch, three geometric models are tested: idealized bifurcation with the branch angle of 60° and 90°, and a realistic shape of the bifurcation.