Interaction of weak shocks in drift-flux model of compressible two-phase flows

Kuila, Sahadeb; Sekhar, T. Raja

doi:10.1016/j.chaos.2017.12.030

Cited by 20 publications

(5 citation statements)

References 15 publications

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“…Another approach to finding self-similarity solutions was used in [8], in which authors applied the Lie group transformations to the non-ideal dusty gas model. The self-similarity zero-viscosity solutions were obtained by [9] with the same methodology of Lie group transformations.…”

Section: Introductionmentioning

confidence: 99%

New Results for Riemann Solution of the Cargo-LeRoux Model by the Application of Flux-Limiter Schemes

Ahmed

2024

VFAST trans. math.

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The Rienamm solution of the Cargo-LeRoux model has been recently introduced in [1] in which authors have found the exact solutions to the initial value problem. This work is the first attempt to apply numerical methods for the Cargo-LeRoux model. The higher-order flux limiter method applied in this paper holds the total variation diminishing property and gives smooth solutions in steep gradient regions. Various limiter functions that lead to different accuracy in numerical results are tested for the Riemann problem. The numerical investigations presented in this work can be used to review limiter-based TVD schemes extensively and to construct a class of highly efficient finite volume/ finite difference methods for such models.

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Section: Introductionmentioning

confidence: 99%

New Results for Riemann Solution of the Cargo-LeRoux Model by the Application of Flux-Limiter Schemes

Ahmed

2024

VFAST trans. math.

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“…Ambika and Radha [36] analyzed the interaction of two weak shocks of the Riemann problem for gas dynamic equations and noticed that the interaction leads to simple wave and shock wave depending on the adiabatic constant. The existence and uniqueness and interactions of weak shock waves of the Riemann solution for drift-flux compressible two-phase flow model and isentropic flux perturbed Cargo-LeRoux model have been explored by Kuila et al [37,38]. Shao [39] investigated whether the Riemann solutions for linearly degenerate hyperbolic conservation laws preserve their global structural stability after minor BV perturbations of the initial data.…”

Section: Introductionmentioning

confidence: 99%

On the Riemann problem and interaction of elementary waves for two‐layered blood flow model through arteries

Jana,

Kuila

2023

Math Methods in App Sciences

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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.

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“…It can be found that the Riemann solutions are stable with respect to small perturbations of the initial data. Wave interactions between weakly nonlinear waves for drift‐flux model of compressible two‐phase flows have been discussed by Kuila and Raja Sekhar 22 . Liu and Sun 23 studied the interactions of the elementary waves of the Aw–Rascle model for the generalized Chaplygin gas.…”

Section: Introductionmentioning

confidence: 99%

Wave interactions in pressureless Cargo–LeRoux model with flux perturbation

Sahoo

Sekhar

2023

Math Methods in App Sciences

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In this article, we discuss the wave interactions in pressureless Cargo-LeRoux model with flux perturbation. The corresponding Riemann solution in terms of a one-parameter family of curves is presented. We prove the existence and uniqueness of the solution to the Riemann problem and construct estimates for the components of the solution. Relevant amplitudes are determined while presenting the interactions of weak discontinuity with contact discontinuity and shock waves. Further, we discuss the interaction of weak shocks in detail. Finally, some test cases are treated to understand the effect of initial data and strength of the shock on the transmitted, reflected amplitudes, and jump in the acceleration of the shock.

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Interaction of weak shocks in drift-flux model of compressible two-phase flows

Cited by 20 publications

References 15 publications

New Results for Riemann Solution of the Cargo-LeRoux Model by the Application of Flux-Limiter Schemes

New Results for Riemann Solution of the Cargo-LeRoux Model by the Application of Flux-Limiter Schemes

On the Riemann problem and interaction of elementary waves for two‐layered blood flow model through arteries

Wave interactions in pressureless Cargo–LeRoux model with flux perturbation

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