1. Riemann solutions of two-layered blood flow model in arteries.
- Author
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Jana, Sumita and Kuila, Sahadeb
- Subjects
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BLOOD flow , *HYPERBOLIC differential equations , *RIEMANN-Hilbert problems , *PARTIAL differential equations , *ALGEBRAIC equations - Abstract
This study investigates the solutions of the Riemann problem for a two-layered blood flow model which is modeled by a system of quasi-linear hyperbolic partial differential equations (PDEs) obtained by vertically averaging the Euler equations over each layer. We explore the elementary waves, namely shock wave, rarefaction wave and contact discontinuity wave on the basis of method of characteristics. Further, we establish the existence and uniqueness of the corresponding local Riemann solution. Across the contact discontinuity wave, the areas of two nonlinear algebraic equations are determined by using the Newton–Raphson method of two variables in all possible wave combinations. A precise analytical method is used to display a detailed vision of the solution for this model inside a specified space domain and some certain time frame. • The Riemann problem for the two-layered blood flow model in arteries is considered. • The Riemann solution is derived analytically using the method of characteristics. • The properties of elementary waves are analyzed. • The existence and uniqueness of this solution is established. • The physical quantities for all four possible wave combinations are displayed in numerical simulation. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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