A Modified “coarse particle” method for calculating non-stationary wave processes in multiphase dispersive media

Губайдуллин, А. А.; Ivandaev, A. I.; Нигматулин, Р. И.

doi:10.1016/0041-5553(77)90183-5

Cited by 13 publications

(4 citation statements)

References 6 publications

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“…The system of hyperbolic equations (1) and (2) was solved by a modified method of "coarse particles" with the first order of accuracy [4]. Artificial viscosity in the form proposed in [5] was used to calculate flows with shock waves.…”

Section: Physicomathematical Formulation Of the Problemmentioning

confidence: 99%

Interaction of rarefaction waves with a finite-thickness layer near a rigid boundary. Equilibrium approximation

Жилин

Федоров

2007

Combust Explos Shock Waves

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Interaction of a rarefaction wave with a layer of solid particles near the end face of a shock tube is considered. A one-dimensional unsteady approximation of mechanics of heterogeneous media with identical pressures of the phases and with allowance for a finite volume concentration of particles in the layer is used as a mathematical model. The wave pattern of the flow and the mechanism of wave interaction with the layer, including the dynamics of the layer boundary depending on the layer thickness and rarefaction-wave width, are determined. The mathematical model proposed is verified against the dependence of the layer-boundary coordinate on time and also the dependence of the velocity of upward motion of the layer on the difference in pressures between the high-pressure and low-pressure chambers.

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Section: Physicomathematical Formulation Of the Problemmentioning

confidence: 99%

Interaction of rarefaction waves with a finite-thickness layer near a rigid boundary. Equilibrium approximation

Жилин

Федоров

2007

Combust Explos Shock Waves

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“…Attempts to modify this theory by taking into account the relative gas stream though the bubbles while maintaining the principal assumption u d =u, (so that u = U,(I+m~)+~Ub , where m is a parameter), begun by Grace and Clift [6], were unsuccessful, as was demonstrated by Davidson and Harrison [7]. Investigations in which the inadequacy of the two-phase theory was explained by pointing out that in reality u d > u, [8,9] permitted a number of empirical conclusions but they did not lead to the establishment of dependences of a sufficiently general nature.…”

Section: Literature Citedmentioning

confidence: 99%

“…At present, in solving a number of problems of aero-and gasdynamics [1][2][3][4], simulating non-steady-state explosive processes [5,6], the dynamics of plasma erosion flares [7,8], wave processes in multiphase media [9], various non-steady-state jet flows of gas and plasma [10][11][12][13], and other problems of engineering physics, the numerical method of large particles [i] is used. To a certain extent, the accuracy of the results obtained by this method was investigated in [1- 4,6,9,[11][12][13] where the obtained numerical results were compared with calculations carried out by other methods, with experimental data, and with the accurate solutions of modeling problems However, in these and in many other works (as an example of univariate calculations we might point out [14,15]), which investigated in detail the accuracy of various finite-difference approaches, the question of the influence of the numerical values of the parameters to be determined, of the intensity of the process, of the thermodynamic state of the medium on the accuracy of the calculation was not analyzed.…”

mentioning

confidence: 99%

Accuracy of calculating flows upon disappearance of discontinuity by the method of large particles

Romanov¹,

Urban²

1981

Journal of Engineering Physics

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“…2. For numerical calculations of initial-boundary problem (1), (2) from [1], we used a modified method of "coarse particles" [5]. The finite-difference equations for determining the velocities at the intermediate time layer with account of the buoyancy force, the expression for determining the volume concentration of the heavy component at the new time layer, and the stability conditions can be found in [6]; we also used the artificial viscosity introduced by Fedorenko [7].…”

mentioning

confidence: 99%

Reflection of shock waves from a solid boundary in a mixture of condensed materials 2. Nonequilibrium approximation

Жилин¹,

Федоров²

1999

J Appl Mech Tech Phys

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depending on the initial parameters of the mixture. A dispersed-frozen SW is reflected by an SW of the same type with slight changes in the velocity and pressure profiles. A frozen SW of the two-front configuration can be reflected as an SW of the dispersed-frozen type or a frozen SW of the two-wave configuration. It is shown that a boundary layer is formed near the wall, where the volume concentration and the density of the light component exceed the corresponding values behind the reflected SW.We discuss the results of numerical calculations of initial-boundary problems (1), (2) from [1] performed in the nonequilibrium approximation and studied within the framework of the equilibrium model. As in [1], all the quantities are presented in the dimensionless form.First of all, we present some results [2-4] concerning possible types of shock waves interacting with the solid walt, which will be needed in what follows. Figure 1 shows a chart of solutions for the incident and reflected shock waves in the plane of the initial volume concentration ml0 and SW velocity ]D I (we note that the equilibrium velocities Ce,0, Ce,fin, and Ce~ in this plane merge into one line C,). In particular, the typical feature of the regions Ill and I12 is the presence of unstable flow in the form of a rarefaction shock wave, where u0-D < ufin-D. In the regions I21 and I31, the incident SW has a fully dispersed structure with either monotonic velocity profiles of the components, or a nonmonotonic velocity profile for the light component with a local minimum and a monotonically decreasing profile for the heavy component. In the regions I22 and /32, the incident shock waves have monotonically decreasing velocity profiles in the heavy component. Concerning the light component, an SW of low amplitude has a monotonically decreasing velocity profile both in front of and behind the internal discontinuity, whereas for an SW with a higher amplitude, the velocity of the light component increases behind the discontinuity to the final equilibrium state. In the regions I41 and I51, the incident shock waves have a bow SW in the second component supplemented by the relaxation zone, where the velocity decreases monotonically to the final equilibrium state, and a continuously decreasing

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A Modified “coarse particle” method for calculating non-stationary wave processes in multiphase dispersive media

Cited by 13 publications

References 6 publications

Interaction of rarefaction waves with a finite-thickness layer near a rigid boundary. Equilibrium approximation

Interaction of rarefaction waves with a finite-thickness layer near a rigid boundary. Equilibrium approximation

Accuracy of calculating flows upon disappearance of discontinuity by the method of large particles

Reflection of shock waves from a solid boundary in a mixture of condensed materials 2. Nonequilibrium approximation

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