A. P. Favorskii

Studying the influence of gravitational overloads on the parameters of blood flow in vessels of greater circulation

The paper is devoted to the numerical modeling of the blood flow in the human cardiovascular system with allowance for gravitational action. A model of the operation of the heart and an equation of state are proposed and studied. Modifications of the graph of the cardiovascular system for the simulation of possible positions of the object in conditions of multifold gravitational overloads are considered.

Mathematical Modeling of Some Applied Problems in Haemodynamics

The present study discusses some basic issues of mathematical modeling in medicine and describes examples of specific results of analytical and numerical investigations in haemodynamics. It briefly describes a method for constructing exact solutions of the linearized equations of haemodynamics on a graph, an analysis of these solutions, and a particular application of the proposed theory for solving practical medical problems. A number of nonspecific aortoarteritis syndromes are simulated. Examples of mathematical modeling of blood flow in the systemic circulatory circuit under the action of a periodically contracting heart are presented. These examples reproduce some of the main physiological regularities of the circulatory system as a whole. One of the applications of mathematical modeling in haemodynamics includes the “stealing” of cerebral blood supply during a temporary occlusion of the subclavian artery.

Quasi-acoustic scheme for the Euler equations of gas dynamics

We suggest an original scheme and an algorithm for the numerical solution of the Euler equations of gas dynamics. The construction of the scheme is based on the mass, momentum, and energy conservation laws. The flux computation is carried out by summation of elementary fluxes formed by small-amplitude running waves that satisfy the linearized equations of gas dynamics. The scheme contains no artificial regularizers, has second-order accuracy on smooth solutions, and is quasimonotone in a neighborhood of the discontinuities. Examples of one- and two-dimensional computations are given.

Computational modeling of the propagation of acoustic pulses in hemodynamics

The present paper deals with the numerical simulation of the propagation of pulses of blood pressure and velocity in a blood vessel. The numerical solution of the system of linear hemodynamic equations is formed as a superposition of progressing waves (Riemann invariants) satisfying the transport equations. Considerable attention is paid to the construction of a difference scheme for the linear and quasilinear transport equations. Examples of computations are presented. The suggested algorithm can be generalized to the case of a quasilinear system of equations.