The generalized Riemann problem for the Chaplygin gas equation

Gupta, Pradeep Kumar; Chaturvedi, Rahul Kumar; Singh, L. P.

doi:10.1016/j.euromechflu.2020.03.001

Cited by 8 publications

(2 citation statements)

References 22 publications

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“…Moreover, this scheme is robust and efficient tool for solving many other hyperbolic systems of conservation laws, like the Ripa model, 40 the blood flow in human artery, 41 and the Chaplygin gas model. 42 Actually, the presented results can be described the isothermal Euler equations with phase transition between a liquid and a vapor phase. 43 We write equation ( 4) in a conserved form…”

Section: Introductionmentioning

confidence: 99%

Simulating isothermal Euler model with non-vacuum initial data via mR scheme

Abdelrahman

Alkhidhr

Mohamed

2022

Journal of Low Frequency Noise, Vibration and Active Control

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We consider the isothermal Euler model with non-vacuum initial data. We extract the Riemann invariants of the isothermal Euler model, which admits vital applications. We also design the modified Rusanov (mR) scheme to solve the isothermal Euler model. This scheme consists of two steps, the first step of the scheme depends on a local parameter allowing to control diffusion. The second stage recovers conservation equation. This technique is a straightforward to implement and precise. We compare this scheme with the Rusanov scheme via three numerical examples. This numerical study verifies the efficiency of the mR scheme. Finally, the mR scheme can be used to solve many other models in applied science.

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Section: Introductionmentioning

confidence: 99%

Simulating isothermal Euler model with non-vacuum initial data via mR scheme

Abdelrahman

Alkhidhr

Mohamed

2022

Journal of Low Frequency Noise, Vibration and Active Control

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“…Also, it has a variety of applications in the field of physical and natural sciences. Many researchers have recently used the differential constraint approach to achieve the precise solution of the hyperbolic system [7] connected by elementary waves (see [8,9]). The differential constraint method is one of the best reduction methods for obtaining particular exact solutions of quasi-linear PDEs.…”

Section: Introductionmentioning

confidence: 99%

The application of differential constraint method for the solution of non-homogeneous generalized Riemann problem

Gaurav,

Singh,

Pradeep

2023

Phys. Scr.

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This paper reports the solution to the Non-homogeneous Riemannproblem by applying the approach of differential constraint for the one-dimensional(1 − D) generalized Chaplygin gas equations with non-constant initial data. Herewe take source term as a Coulomb type constant frictional term. We reducedthe governing non-homogeneous model into a homogeneous one by introducing anew velocity variable. By virtue of this advantage of frictional type source term,we would easily determine the solution of reformulated homogeneous governingmodel. We have computed the differential constraint and its consistency condi-tions for the specified model. Moreover, we have derived here the compatibilitycondition between the governing model and the differential constraints. The solu-tions to generalized Riemann problem for the 1 − D Euler’s equation of governinggas model are obtained as well as for the smooth and non-constant initial condi-tions the comprehensive overview of the solutions is studied.

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Riemann problem for the Chaplygin gas equations for several classes of non-constant initial data

Kumar

Radha

2022

European Journal of Mechanics - B/Fluids

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The generalized Riemann problem for the Chaplygin gas equation

Cited by 8 publications

References 22 publications

Simulating isothermal Euler model with non-vacuum initial data via mR scheme

Simulating isothermal Euler model with non-vacuum initial data via mR scheme

The application of differential constraint method for the solution of non-homogeneous generalized Riemann problem

Riemann problem for the Chaplygin gas equations for several classes of non-constant initial data

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