Mathematical modelling of hemodynamics of large blood vessels

A brief overview of mathematical models of contemporary applied hemodynamics is given. The special attention is paid to questions of development of effective computational algorithms implementing one-dimensional model. For this purpose TVD-monotonized schemes having the second order accuracy both in time and space are used. A number of test problems with analytical solutions are proposed. Questions of convergence and a choice of grid parameters for various schemes are investigated. The approaches using multiscale hemodynamics models are considered. An embedding of one-dimensional model of a single vessel into 0-dimensional model of vascular system is implemented. The possibility of using linear model for considered class problems of hemodynamics is analyzed.