Solution of the Riemann problem for an ideal polytropic dusty gas in magnetogasdynamics

2020 ◽  
Vol 75 (6) ◽  
pp. 511-522 ◽  
Author(s):  
Astha Chauhan ◽  
Rajan Arora
Keyword(s):  
Riemann Problem ◽  
Solid Particles ◽  
Dusty Gas ◽  
Rarefaction Waves ◽  
Linear System Of Equations ◽  
Simple Waves ◽  
Elementary Wave ◽  
The One ◽  
Quasi Linear System ◽  
Elementary Waves

AbstractThe main aim of this paper is, to obtain the analytical solution of the Riemann problem for a quasi-linear system of equations, which describe the one-dimensional unsteady flow of an ideal polytropic dusty gas in magnetogasdynamics without any restriction on the initial data. By using the Rankine-Hugoniot (R-H) and Lax conditions, the explicit expressions of elementary wave solutions (i. e., shock waves, simple waves and contact discontinuities) are derived. In the flow field, the velocity and density distributions for the compressive and rarefaction waves are discussed and shown graphically. It is also shown how the presence of small solid particles and magnetic field affect the velocity and density across the elementary waves. It is an interesting fact about this study that the results obtained for the Riemann problem are in closed form.

A Second-Order Cell-Centered Lagrangian Method for Two-Dimensional Elastic-Plastic Flows

2017 ◽  
Vol 22 (5) ◽  
pp. 1224-1257 ◽  
Author(s):  
Jun-Bo Cheng ◽  
Yueling Jia ◽  
Song Jiang ◽  
Eleuterio F. Toro ◽  
Ming Yu
Keyword(s):  
Constitutive Model ◽  
Riemann Problem ◽  
Wave Structure ◽  
Solution Procedure ◽  
Second Order ◽  
Rarefaction Waves ◽  
Elastic Plastic ◽  
Yielding Condition ◽  
Nested Iterations ◽  
Von Mises

AbstractFor 2D elastic-plastic flows with the hypo-elastic constitutive model and von Mises’ yielding condition, the non-conservative character of the hypo-elastic constitutive model and the von Mises’ yielding condition make the construction of the solution to the Riemann problem a challenging task. In this paper, we first analyze the wave structure of the Riemann problem and develop accordingly aFour-Rarefaction wave approximateRiemannSolver withElastic waves (FRRSE). In the construction of FRRSE one needs to use an iterative method. A direct iteration procedure for four variables is complex and computationally expensive. In order to simplify the solution procedure we develop an iteration based on two nested iterations upon two variables, and our iteration method is simple in implementation and efficient. Based on FRRSE as a building block, we propose a 2nd-order cell-centered Lagrangian numerical scheme. Numerical results with smooth solutions show that the scheme is of second-order accuracy. Moreover, a number of numerical experiments with shock and rarefaction waves demonstrate the scheme is essentially non-oscillatory and appears to be convergent. For shock waves the present scheme has comparable accuracy to that of the scheme developed by Maire et al., while it is more accurate in resolving rarefaction waves.

The Effect of the Microstructure of Semisolid Al Alloy on its Rheology

2014 ◽  
Vol 490-491 ◽  
pp. 109-112
Author(s):  
De Wen Cao ◽  
Jia Huan Wang ◽  
Yu Qing Sun ◽  
Ke Hua Chen ◽  
Cheng Ming Yu ◽  
...  
Keyword(s):  
Particle Size ◽  
Rheological Behavior ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Alloy System ◽  
The State ◽  
Solid Particles ◽  
Al Alloy ◽  
Agglomerate Size ◽  
The One

In the present work, the effect of the microstructure of AlSi6Mg2 alloy on its macro-rheological behavior of the steady AlSi6Mg2 alloy is investigated. Specifically, the effect of particle size, packing mode and degree of the agglomeration of particles are analyzed. It can be seen that the apparent viscosity decreases with increasing the particle size (d) ifdis between a few μm and 200 μm, while the solid particle size does not affect viscosity except this region. This theoretical prediction is in qualitatively agreement with the experimental data. The trend of the variation of the average agglomerate size with the particle size is the same as the one of viscosity. The packing mode of solid particles in agglomerate is closely related to the solid volume fraction and the characteristics of the alloy system. Subsequently, the state of agglomeration of solid particles which determines the rheology of semisolid AlSi6Mg2 alloy, while the external flow conditions (such as shear rate) influence the viscosity by changing the state of agglomeration. Consequently, the particle size, the packing mode and the average agglomerate size have different effect on the rheological behavior of SSMS.

Interaction of rarefaction waves with area reductions in ducts

1983 ◽  
Vol 137 ◽  
pp. 285-305 ◽  
Author(s):  
J. J. Gottlieb ◽  
O. Igra
Keyword(s):  
Steady Flow ◽  
Rarefaction Wave ◽  
Gas Flow ◽  
Flow Analysis ◽  
Inviscid Flow ◽  
Rarefaction Waves ◽  
Area Reduction ◽  
Random Choice Method ◽  
Wave Patterns ◽  
The One

The interaction of a rarefaction wave with a gradual monotonic area reduction of finite length in a duct, which produces transmitted and reflected rarefaction waves and other possible rarefaction and shock waves, was studied both analytically and numerically. A quasi-steady flow analysis which is analytical for an inviscid flow of a perfect gas was used first to determine the domains of and boundaries between four different wave patterns that occur at late times, after all local transient disturbances from the interaction process have subsided. These boundaries and the final constant strengths of the transmitted, reflected and other waves are shown as a function of both the incident rarefaction-wave strength and area-reduction ratio, for the case of diatomic gases and air with a specific-heat ratio of 7/5. The random-choice method was then used to solve numerically the conservation equations governing the one-dimensional non-stationary gas flow for many different combinations of rarefaction-wave strengths and area-reduction ratios. These numerical results show clearly how the transmitted, reflected and other waves develop and evolve with time, until they eventually attain constant strengths, in agreement with quasi-steady flow predictions for the asymptotic wave patterns. Note that in all of this work the gas in the area reduction is initially at rest.

scholarly journals An improved exact Riemann solver for relativistic hydrodynamics

2001 ◽  
Vol 449 ◽  
pp. 395-411 ◽  
Author(s):  
LUCIANO REZZOLLA ◽  
OLINDO ZANOTTI
Keyword(s):  
Riemann Problem ◽  
Initial Conditions ◽  
Wave Pattern ◽  
Initial Guess ◽  
Relativistic Velocity ◽  
Riemann Solver ◽  
Rarefaction Waves ◽  
Riemann Solvers ◽  
Velocity Jump ◽  
Exact Riemann Solver

A Riemann problem with prescribed initial conditions will produce one of three possible wave patterns corresponding to the propagation of the different discontinuities that will be produced once the system is allowed to relax. In general, when solving the Riemann problem numerically, the determination of the specific wave pattern produced is obtained through some initial guess which can be successively discarded or improved. We here discuss a new procedure, suitable for implementation in an exact Riemann solver in one dimension, which removes the initial ambiguity in the wave pattern. In particular we focus our attention on the relativistic velocity jump between the two initial states and use this to determine, through some analytic conditions, the wave pattern produced by the decay of the initial discontinuity. The exact Riemann problem is then solved by means of calculating the root of a nonlinear equation. Interestingly, in the case of two rarefaction waves, this root can even be found analytically. Our procedure is straightforward to implement numerically and improves the efficiency of numerical codes based on exact Riemann solvers.

The wave equation for spin 1 in Hamiltonian form. II

1955 ◽  
Vol 232 (1191) ◽  
pp. 435-447 ◽  
Keyword(s):  
Hermitian Form ◽  
Expectation Value ◽  
Charge Quantization ◽  
Elementary Wave ◽  
Energy Aspect ◽  
Magnetic Spin ◽  
The Mean ◽  
The One ◽  
Energy And Momentum ◽  
General Association

The investigation is mainly concerned with the relation between constants of the motion and the conservation laws in differential form. The operator that commutes with the Hamiltonian is not the one whose Hermitian form obeys a conservation law and therefore yields, on integration over space, the mean (or expectation) value of the constant. There is a general association between the ‘commuting’ and the ‘conserved’ operators; the latter does not in general commute with the Hamiltonian. The duplication stems from normalizing by a non-definite Hermitic form, meaning the charge density. It entails that an elementary wave always carries a positive amount of energy, and a momentum in the direction in which the wave proceeds, though from the eigenvalues of energy and momentum one might expect either sign. A deep-rooted general connexion between charge quantization and the energy aspect of frequency is suggested. An attempt is made to clarify the relation between mechanical and magnetic spin, the latter appearing to depend in a simple way on the fifth Kemmer matrix.

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