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In this paper, we focus on the Riemann problem for two‐layered blood flow model, which is represented by a system of quasi‐linear hyperbolic partial differential equations (PDEs) derived from the Euler equations by vertical averaging across each layer. We consider the Riemann problem with varying velocities and equal constant density through arteries. For instance, the flow layer close to the wall of vessel has a slower average speed than the layer far from the vessel because of the viscous effect of the blood vessel. We first establish the existence and uniqueness of the corresponding Riemann solution by a thorough investigation of the properties of elementary waves, namely, shock wave, rarefaction wave, and contact discontinuity wave. Further, we extensively analyze the elementary wave interaction between rarefaction wave and shock wave with contact discontinuity and rarefaction wave and shock wave. The global structure of the Riemann solutions after each wave interaction is explicitly constructed and graphically illustrated towards the end. [ABSTRACT FROM AUTHOR]

In this paper, we explore the weak shock wave interactions in isentropic Cargo‐LeRoux model of flux perturbation which describes strictly hyperbolic quasilinear system of conservation laws. For the Riemann problem, we provide a global existence and uniqueness result of exact solution. Further, we establish the exact solution explicitly in terms of one parameter family of elementary wave curves. We devise a necessary and sufficient condition on initial data for which the solution of the Riemann problem consists of either a shock wave or a simple wave according to one and three family of characteristic curves. Lastly, we analyze the Von Neumann result related to collision of weak shock waves of same family. [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 this paper, we consider the Riemann problem for a five-equation, two-pressure (5E2P) model proposed by Ransom and Hicks for an isentropic compressible gas-liquid two-phase flows. The model is given by a strictly hyperbolic, non-conservative system of five partial differential equations (PDEs). We investigate the structure of the Riemann problem and construct an approximate solution for it. We solve the Riemann problem for this model approximately assuming that all waves corresponding to the genuinely nonlinear characteristic fields are rarefaction and discuss their properties. To verify the solver, a series of test problems selected from the literature are presented. [ABSTRACT FROM AUTHOR]

We consider the Riemann problem for a five-equation, two-pressure (5E2P) model of non-ideal isentropic compressible gas–liquid two-phase flows. This system is more complex due to the extended thermodynamics model for van der Waals gases, that is, typical real gases for gas phase and Tait׳s equation of state for liquid phase. The overall model is strictly hyperbolic and non-conservative form. We investigate the structure of Riemann problem and construct the solution for it. To construct solution of Riemann problem approximately assuming that all waves corresponding to the genuinely non-linear characteristic fields are rarefaction and then we discuss their properties. Lastly, we discuss numerical examples and study the solution influenced by the van der Waals excluded volume. [ABSTRACT FROM AUTHOR]

In this paper we analyze the Riemann problem for the widely used drift-flux two-phase flow model. This analysis introduces the complete information that is attained in the representation of solutions to the Riemann problem. It turns out that the Riemann waves have rarefactions, a contact discontinuity and shocks. Within this respect, an exact Riemann solver is developed to accurately resolve and represent the complete wave structure of the gas-liquid two-phase flows. To verify the solver, a series of test problems selected from the literature are presented including validation against independent numerical simulations where the solution of the Riemann problem is fully numerical. In this framework the governing equations are discretized by finite volume techniques facilitating the application Godunov methods of centred-type. It is shown that both analytical and numerical results demonstrate the broad applicability and robustness of the new exact Riemann solver. [ABSTRACT FROM AUTHOR]