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In this paper, we concern about the Riemann problem for compressible no‐slip drift‐flux model which represents a system of quasi‐linear partial differential equations derived by averaging the mass and momentum conservation laws with modified Chaplygin two‐phase flows. We obtain the exact solution of Riemann problem by elaborately analyzing characteristic fields and discuss the elementary waves namely, shock wave, rarefaction wave and contact discontinuity wave. By employing the equality of pressure and velocity across the middle characteristic field, two nonlinear algebraic equations with two unknowns as gas density ahead and behind the middle wave are formed. The Newton–Raphson method of two variables is applied to find the unknowns with a series of initial data from the literature. Finally, the exact solution for the physical quantities such as gas density, liquid density, velocity, and pressure are illustrated graphically. [ABSTRACT FROM AUTHOR]

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]

In the present paper, we study the Riemann problem for quasilinear hyperbolic system of partial differential equations governing the one dimensional non-ideal isentropic magnetogasdynamics with transverse magnetic field. We discuss the properties of rarefaction waves, shocks and contact discontinuities. Differently from single equation methods rooted in the ideal gasdynamics, the new approach is based on the system of two nonlinear algebraic equations imposing the equality of total pressure and velocity, assuming as unknowns the two values of densities, on both sides of the contact discontinuity. Newton iterative method is used to obtain densities. The resulting exact solver is implemented with the examples of general applicability of the proposed approach. [ABSTRACT FROM AUTHOR]