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1.
Nonlinear gas oscillations in a closed tube driven by the aperiodic motions of a piston as a result of the action of the external
and internal pressure drop are studied. The external pressure takes two values alternating at the moment of change of direction
of motion of the piston. Two models of the motion of the gas are considered. Model 1 is formed by a system of equations representing
the mass, momentum, and entropy conservation laws. As distinct from model 1, model 2 includes the total energy conservation
law in place of the entropy conservation laws.
Kazan’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 134–142, March–April, 1998.
The work was carried out with partial support from the Russian Foundation for Fundamental Research (project No. 96-01-00484). 相似文献
2.
V. M. Teshukov 《Journal of Applied Mechanics and Technical Physics》2007,48(3):303-309
The classical shallow-water equations describing the propagation of long waves in flow without a shear of the horizontal velocity
along the vertical coincide with the equations describing the isentropic motion of a polytropic gas for a polytropic exponent
γ = 2 (in the theory of fluid wave motion, this fact is called the gas-dynamic analogy). A new mathematical model of long-wave
theory is derived that describes shear free-boundary fluid flows. It is shown that in the case of one-dimensional motion,
the equations of the new model coincide with the equations describing nonisentropic gas motion with a special choice of the
equation of state, and in the multidimensional case, the new system of long-wave equations differs significantly from the
gas motion model. In the general case, it is established that the system of equations derived is a hyperbolic system. The
velocities of propagation of wave perturbations are found.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 8–15, May–June, 2007. 相似文献
3.
A general approach to the construction of conservation laws for classical nonconservative dynamical systems is presented. The conservation laws are constructed by finding corresponding integrating factors for the equations of motion. Necessary conditions for existence of the conservation laws are studied in detail. A connection between an a priori known conservation law and the corresponding integrating factors is established. The theory is applied to two particular problems. 相似文献
4.
Yu. A. Chirkunov 《Journal of Applied Mechanics and Technical Physics》2009,50(2):213-219
An algorithm is proposed which allows all conservation laws for a system of differential equations to be to obtained from
its one zero-order conservation law for which the general rank of the Jacobi matrix is equal to the number of independent
variables of the system. The efficiency of the algorithm is shown by examples of the equations of gas dynamics, for which
new conservation laws are derived. For the equations considered, additional symmetry properties related to these conservation
laws are established.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 53–60, March–April, 2009. 相似文献
5.
We study the model describing thermal motion of gas in the rarefied space. This model can be used, in particular, in the study of the state of the medium behind the front of shock wave after very strong blast, in the study of the processes taking place inside of tornado, in the study of the motion of the gas in outer space. For any given initial distribution of the pressure a specific selection of mass Lagrange variables leads to reduction of the system of differential equations describing this motion to the system, for which the number of independent variables is less on the unit. For the obtained system we found all nontrivial conservation laws of the first order. In addition to the classical conservation laws the system has other conservation laws, which generalizes the energy conservation law. We obtained the exact solutions of this system. These solutions describe a variety of different physical processes taking place in the rarefied medium. Using the symmetry properties of the system we got the generating formulas for the receipt of the new solutions using already found earlier solutions of the system. 相似文献
6.
Denis Serre 《Archive for Rational Mechanics and Analysis》2016,219(2):679-699
We study the long-time stability of shock-free solutions of hyperbolic systems of conservation laws, under an arbitrarily large initial disturbance in L 2∩ L ∞. We use the relative entropy method, a robust tool which allows us to consider rough and large disturbances. We display practical examples in several space dimensions, for scalar equations as well as isentropic gas dynamics. For full gas dynamics, we use a trick from Chen [1], in which the estimate is made in terms of the relative mechanical energy instead of the relative mathematical entropy. 相似文献
7.
Dai Tian-min 《应用数学和力学(英文版)》2003,24(10):1126-1133
The purpose is to reestablish the balance laws of momentum, angular momentum and energy and to derive the corresponding local
and nonlocal balance equations for micromorphic continuum mechanics and couple stress theory. The desired results for micromorphic
continuum mechanics and couple stress theory are naturally obtained via direct transitions and reductions from the coupled
conservation law of energy for micropolar continuum theory, respectively. The basic balance laws and equations for micromorphic
continuum mechanics and couple stress theory are constituted by combining these results derived here and the traditional conservation
laws and equations of mass and microinertia and the entropy inequality. The incomplete degrees of the former related continuum
theories are clarified. Finally, some special cases are conveniently derived.
Foundation items: the National Natural Science Foundation of China (10072024); the Research Foundation of Liaoning Education Committee (990111001)
Biography: DAI Tian-min (1931≈) 相似文献
8.
LIU Peiqing 《力学与实践》1979,42(3):277
严格而言,流体力学中所有守恒定律均是针对物质体系的(或称流体系统),如质量、动量、动量矩和能量等守恒定律。如果跟随物质体系描述和表征流体质点系的运动行为,即为Lagrange描述方法;如果把物质体系的运动和守恒定律转换到空间坐标系中,即为人们常说的Euler描述方法。因此,对于具体考察(跟随的)的流体物质系统而言,各守恒定律存在由物质体系表征到空间体系表征的转换,这个转换关系就是著名的Reynolds输运方程。本文从动边界微积分关系式出发,系统推导了在不同运动速度控制体上的雷诺输运方程,并通过讨论进一步阐明各种不同形式输运方程的物理意义。 相似文献
9.
Dai Tian-min 《应用数学和力学(英文版)》2003,24(10):1134-1140
The existing various couple stress theories have been carefully restudied.The purpose is to propose a coupled Noether’s theorem and to reestablish rather complete conservation laws and balance equations for couple stress elastodynamics. The new concrete forms of various conservation laws of couple stress elasticity are derived. The precise nature of these conservation laws which result from the given invariance requirements are established. Various special cases are reduced and the results of micropolar continua may be naturally transited from the results presented in this paper. 相似文献
10.
Dai Tian-min 《应用数学和力学(英文版)》2003,24(12):1369-1374
The purpose is to reestablish the coupled conservation laws, the local conservation equations and the jump conditions of mass
and inertia for polar continuum theories. In this connection the new material derivatives of the deformation gradient, the
line element, the surface element and the volume element were derived and the generalized Reynolds transport theorem was presented.
Combining, these conservation laws of mass and inertia with the balance laws of momentum, angular momentum and energy derived
in our previous papers of this series, a rather complete system of coupled basic laws and principles for polar continuum theories
is constituted on the whole. From this system the coupled nonlocal balance equations of mass, inertia, momentum, angular momentum
and energy may be obtained by the usual localization.
Contributed by DAI Tian-min, Original Member of Editorial Committee, AMM
Foundation items: the National Natural Science Foundation of China (10072024); the Research Foundation of Liaoning Education Committee (990111001)
Biography: DAI Tian-min (1931≈) 相似文献
11.
B. N. Elemesova 《Journal of Applied Mechanics and Technical Physics》1999,40(1):28-35
The plane-parallel unsteady-state shear gas flow in a narrow channel of constant cross section is considered. The existence
theorem of solutions in the form of simple waves of a set of equations of motion is proved for a class of isentropic flows
with a monotone velocity profile over the channel depth. The exact solution described by incomplete beta-functions is found
for a polytropic equation of state in a class of isentropic flows.
Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from
Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 36–43, January–February, 1999. 相似文献
12.
13.
On the basis of the work [P.‐H. Maire, R. Abgrall, J. Breil, J. Ovadia, SIAM J. Sci. Comput. 29 (2007), 1781–1824], we present an entropy fixed cell‐centered Lagrangian scheme for solving the Euler equations of compressible gas dynamics. The scheme uses the fully Lagrangian form of the gas dynamics equations, in which the primary variables are cell‐centered. And using the nodal solver, we obtain the nodal viscous‐velocity, viscous‐pressures, antidissipation velocity, and antidissipation pressures of each node. The final nodal velocity is computed as a weighted sum of viscous‐velocity and antidissipation velocity, so do nodal pressures, whereas these weights are calculated through the total entropy conservation for isentropic flows. Consequently, the constructed scheme is conservative in mass, momentum, and energy; preserves entropy for isentropic flows, and satisfies a local entropy inequality for nonisentropic flows. One‐ and two‐dimensional numerical examples are presented to demonstrate theoretical analysis and performance of the scheme in terms of accuracy and robustness.Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
14.
V. V. Pukhnachev 《Journal of Applied Mechanics and Technical Physics》2004,45(2):167-171
This paper studies integral relations to which the solutions of the Navier–Stokes equations or Euler equations satisfy in the case of fluids filling the entire threedimensional space. The existence of these relations is due to a rapid decrease of the velocity field at infinity (but not too rapid in order that the required asymptotic forms are reproduced with time). Of special interest are the integrals of motion whose density depends quadratically on the velocities or their derivative with respect to the coordinates. Such integrals (conservation laws) for the Navier–Stokes equations were recently found by Dobrokhotov and Shafarevich. In the present paper, new conservation laws are obtained, which are quadratic in the derivatives of the velocity and lead to identities that link the averaged and pulsation characteristics of ree turbulent flows. 相似文献
15.
L. V. Ovsyannikov 《Journal of Applied Mechanics and Technical Physics》2000,41(5):865-869
It is shown that a periodic two-dimensional isentropic motion of a gas exists and it is described by an exact solution of
the equations of gas dynamics. A polytropic gas that fills a circular cylinder rotates and oscillates (in the radial direction)
simultaneously under the action of periodically changing external pressure. The solution obtained belongs to the class of
solutions with a velocity field that is linear in the coordinates (with homogeneous deformation).
Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from
Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 5, pp. 115–119, September–October, 2000. 相似文献
16.
V. M. Teshukov 《Journal of Applied Mechanics and Technical Physics》1999,40(2):263-275
Generalized characteristics and Riemann invariants that are preserved along the characteristics are found for a kinetic model
of motion of bubbles in a fluid. Conditions that ensure the hyperbolicity of a set of equations of a bubbly flow are obtained.
It is shown that the set of equations of motion has an infinite number of conservation laws. An infinite series of generalized
symmetries admitted by the equations is constructed. Solutions that are invariant under the generalized symmetries of solution
and describe the propagation of running and simple waves in a bubbly fluid are found.
Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from
Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No., 2. pp. 86–100, March–April, 1999. 相似文献
17.
Based on the laws of conservation of mass, momentum, and energy, equations of dynamics of multiphase systems, which are gas mixtures with hollow microspheres with selectively permeable shells, are obtained under the assumption of quasisteadiness of the process offilling the microspheres by the gas. Acoustic characteristics of the system composed of a uniform gas and hollow permeable microspheres are studied using a simplified (onevelocity and onetemperature) model. The frequency dependences of velocity and damping coefficient of sound are determined with regard for gas density (pressure) relaxation inside the microspheres. 相似文献
18.
A large class of wave equations, with dissipation and source terms (Gordon type equations), are analysed using a symmetry
approach and constructing conservation laws. We obtain some, previously unknown, relationships between the conservation laws
and symmetries in the former case. In the latter case, we use the multiplier (and homotopy) approach to construct conservation
laws from which some surprisingly, interesting higher-order variational symmetries and corresponding conserved quantities
are obtained for a large class of Gordon type equations similar to those of the sine-Gordon equation. 相似文献
19.
T. R. Amanbaev 《Journal of Applied Mechanics and Technical Physics》2003,44(5):634-639
The gas flow in plane shock waves slipping along an impermeable surface with a rectangular cavity where solid disperse particles are suspended is considered numerically. The motion of the gas and particles (gas suspension) is modeled by equations of mechanics of multiphase media. Some laws of the behavior of the dusty cloud in the cavity are established for the case of wave interaction with the cavity. 相似文献
20.
Shen Hui-chuan 《应用数学和力学(英文版)》1986,7(8):755-766
This work is the continuation of the discussion of Ref. [1]. In this paper we resolve the equations of isentropic gas dynamics into two problems: the three-dimensional non-constant irrotational flow (thus the isentropic flow, too), and the three-dimensional non-constant indivergent flow (i. c. the in compressible isentropic flow). We apply the theory of functions of a complex variable under Dirac-Pauli representation and the Legendre transformation, transform these equations of two problems from physical space into velocity space, and obtain two general Chaplygin equations in this paper. The general Chaplygin equation is a linear difference equation, and its general solution can be expressed at most by the hypergeometric functions. Thus we can obtain the general solution of general problems for the three-dimensional non-constant isentropic flow of gas dynamics. 相似文献