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• W4200283003 abstract "• The 1D models of non-Newtonian hemodynamics are introduced. • The perturbation method is used for the analytical solution of the problems for the inviscid model. • The analytical solutions of the model problems for the infinite, semi-infinite, and finite interval are obtained. • The solutions, obtained for the inviscid and viscid models are compared and the effect of the velocity profile is analyzed. The paper is devoted to the comparison of one-dimensional blood flow models in application to the solution of model problems. In the viscid case, the non-Newtonian properties of blood are considered. Original one-dimensional models, based on the Carreau, Carreau–Yasuda, Cross, and Powell–Eyring rheological models, are constructed by the averaging of the Navier–Stokes equations. The approach to the analytical solution of problems in the inviscid case is proposed. The originality of the method is based on the small perturbation of the initial rest state, corresponding to zero velocity. It leads to the solution of the linear wave equations. The solutions of three problems — for the infinite, semi-infinite, and finite intervals are obtained. The examples are presented for the small parameter value ∼ 10 − 2 . Analytical solutions are used for the comparison of different one-dimensional models of blood flow, where the viscosity (Newtonian and non-Newtonian) is considered. The problems for the viscid models are solved numerically by the third-order WENO scheme. As the results of the comparison of models, the effects of the viscosity and velocity profile are analyzed. From a practical viewpoint, the solutions obtained by the perturbation method can be used for the testing of programs for numerical simulations and for the comparison of different blood flow models." @default.
• W4200283003 created "2021-12-31" @default.
• W4200283003 creator A5003180256 @default.
• W4200283003 date "2022-04-01" @default.
• W4200283003 modified "2023-09-27" @default.
• W4200283003 title "Comparison of inviscid and viscid one-dimensional models of blood flow in arteries" @default.
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• W4200283003 doi "https://doi.org/10.1016/j.amc.2021.126856" @default.
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