Delta Shock Wave Solution of the Riemann Problem for the Non-homogeneous Modified Chaplygin Gasdynamics

Chaturvedi, Rahul Kumar; Singh, L. P.; Zeidan, Dia

doi:10.1007/s10884-020-09914-8

Cited by 10 publications

(4 citation statements)

References 28 publications

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“…Dia Zeidan et al [34][35] studied the evolution of the plane and cylindrical symmetric motion of the gas dynamics equations and discontinuity surfaces using the van der Waals model for magnetic gases. Rahul Kumar Chaturvedi et al 36 also studied the Riemann and non-classical Riemann solutions of the nonsimultaneous partial differential equations for the fluid MCG model, obtaining that the fundamental in the solution waveforms can change due to external forces. For a two-phase fluid (at least one phase is a fluid) as in a suspension model with kinematic coupling, where the flow of one phase always involves the relative motion of the other phase, the numerical solution and characteristics of the two-phase flow equations and the Riemann numerical solution of the compressible twophase flow were studied by D. Zeidan.…”

Section: Mathematical Methods and The Application In Other Fieldsmentioning

confidence: 99%

Research on nonlinear model and fuzzy fractional order PI^λD^μ control of air suspension system

Wang

et al. 2021

Journal of Low Frequency Noise, Vibration and Active Control

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To improve the ride comfort of wheeled armored vehicles, air springs are used. To describe the vehicle motion more accurately, a nine-degree-of-freedom air suspension system for the whole vehicle was established, and its equations of motion were derived. Through theoretical analysis of the stiffness characteristics and forces on the air springs, the nonlinear restoring force was obtained as a cubic polynomial of the air spring displacement. The simulation results obtained by fitting the polynomial and radial basis function curves with MATLAB/Simulink software are consistent with the actual test results, thus verifying the correctness of the nonlinear air spring polynomial model. Finally, a fuzzy fractional order PIλDμ controller is designed and simulated for the vehicle-seat-body model in terms of wheel dynamic load, suspension dynamic deflection, body acceleration, and other indicators. The simulation results show that the fuzzy fractional order PIλDμ Proportion Integral Differential (PID) control strategy has better overall performance than the PID control strategy, fuzzy control strategy, and fuzzy PID control strategy.

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Section: Mathematical Methods and The Application In Other Fieldsmentioning

confidence: 99%

Research on nonlinear model and fuzzy fractional order PI^λD^μ control of air suspension system

Wang

et al. 2021

Journal of Low Frequency Noise, Vibration and Active Control

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“…30 Zafar and Sharma 31 discussed about the classification of the Riemann problem for compressible two-dimensional Euler system in non-ideal gas. For more details on delta shock, we refer to previous works, [32][33][34][35][36] and for classical elementary wave, we refer to Minhajul and Raja Sekhar 37 and Raja Sekhar and Minhajul 38 and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Self‐similar viscosity approach to the Riemann problem for a strictly hyperbolic system of conservation laws

Chhatria

Sen

Sekhar

2022

Math Methods in App Sciences

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Here, we study the Riemann problem for a strictly hyperbolic system of conservation laws, which occurs in gas dynamics and nonlinear elasticity. We establish the existence and uniqueness of the solution of Riemann problem containing delta shock wave by employing self-similar vanishing viscosity approach. We prove that delta shock is stable under self-similar viscosity perturbation, which ensures that delta shock wave is a unique entropy solution.

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“…However, due to consistence and coherence, we expect to encompass relevant numerical applications on finding at least approximate solutions without the need for large computing time and with precise informations on sign and localization. To provide the readers with some references about the numerical and approximation results that can be achieved, we mention the recent papers 17–23 . For example, in Chau et al, 21,22 the Adomian decomposition method is recognized as a key tool for many engineering applications, in computing solutions of nonlinear partial differential equations without a priori information on the investigated equation.…”

Section: Introductionmentioning

confidence: 99%

On (p(x), q(x))‐Laplace equations in ℝN without Ambrosetti‐Rabinowitz condition

Nastasi

2021

Math Methods in App Sciences

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In the present work, we consider a (p(x), q(x))‐elliptic equation describing the behavior of a double‐phase anisotropic problem which has relevance in electrorheological fluid applications. The analysis leads to the existence of weak (nonnegative) solutions in the special case of potential terms with critical frequency and a superlinear reaction term. In order to prove the existence result, we combine critical point theory of mountain pass type with related topological and variational methods. Basically, the approach is variational, but we do not impose any Ambrosetti‐Rabinowitz type condition for the superlinearity of the reaction. More specifically, we apply the Euler‐Lagrange functional approach to the variational formulation of the above‐mentioned model problem. We note that we work in the whole space ℝN and so we have to consider non‐compact embeddings. This aspect constitutes an additional difficulty in our study.

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Delta Shock Wave Solution of the Riemann Problem for the Non-homogeneous Modified Chaplygin Gasdynamics

Cited by 10 publications

References 28 publications

Research on nonlinear model and fuzzy fractional order PI^λD^μ control of air suspension system

Research on nonlinear model and fuzzy fractional order PI^λD^μ control of air suspension system

Self‐similar viscosity approach to the Riemann problem for a strictly hyperbolic system of conservation laws

On (p(x), q(x))‐Laplace equations in ℝN without Ambrosetti‐Rabinowitz condition

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Delta Shock Wave Solution of the Riemann Problem for the Non-homogeneous Modified Chaplygin Gasdynamics

Cited by 10 publications

References 28 publications

Research on nonlinear model and fuzzy fractional order PIλDμ control of air suspension system

Research on nonlinear model and fuzzy fractional order PIλDμ control of air suspension system

Self‐similar viscosity approach to the Riemann problem for a strictly hyperbolic system of conservation laws

On (p(x), q(x))‐Laplace equations in ℝN without Ambrosetti‐Rabinowitz condition

Contact Info

Product

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About

Research on nonlinear model and fuzzy fractional order PI^λD^μ control of air suspension system

Research on nonlinear model and fuzzy fractional order PI^λD^μ control of air suspension system