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1
Content available remote On the evolution of solutions of Burgers equation on the positive quarter-plane
Hanaç Esen
Demonstratio Mathematica
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2019
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Vol. 52, nr 1
237--248
EN
In this paper we investigate an initial-boundary value problem for the Burgers equation on the positive quarter-plane; vt + vvx - vxx = 0, x>0, t>0, v(x,0) = u+, x>0, v(0,t) = ub, t>0, where x and t represent distance and time, respectively, and u+ is an initial condition, ub is a boundary condition which are constants (u+ ≠ ub). Analytic solution of above problem is solved depending on parameters (u+ and ub) then compared with numerical solutions to show there is a good agreement with each solutions.
2
Content available Nonlinear Interaction of Modes in a Planar Flow of a Gas with Viscous and Thermal Attenuation
Perelomova Anna
Archives of Acoustics
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2019
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Vol. 44, No. 3
551--559
EN
The nonlinear interaction of wave and non-wave modes in a gas planar flow are considered. Attention is mainly paid to the case when one sound mode is dominant and excites the counter-propagating sound mode and the entropy mode. The modes are determined by links between perturbations of pressure, density, and fluid velocity. This definition follows from the linear conservation equations in the differentia form and thermodynamic equations of state. The leading order system of coupling equations for interacting modes is derived. It consists of diffusion inhomogeneous equations. The main aim of this study is to identify the principle features of the interaction and to establish individual contributions of attenuation (mechanical and thermal attenuation) in the solution to the system.
3
Content available Impact of Boundary Conditions on Acoustic Excitation of Entropy Perturbations in a Bounded Volume of Newtonian Gas
Perelomova Anna
Archives of Acoustics
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2019
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Vol. 44, No. 2
321--328
EN
Excitation of the entropy mode in the field of intense sound, that is, acoustic heating, is theoretically considered in this work. The dynamic equation for an excess density which specifies the entropy mode, has been obtained by means of the method of projections. It takes the form of the diffusion equation with an acoustic driving force which is quadratically nonlinear in the leading order. The diffusion coefficient is proportional to the thermal conduction, and the acoustic force is proportional to the total attenuation. Theoretical description of instantaneous heating allows to take into account aperiodic and impulsie sounds. Acoustic heating in a half-space and in a planar resonator is discussed. The aim of this study is to evaluate acoustic heating and determine the contribution of thermal conduction and mechanical viscosity in different boundary problems. The conclusions are drawn for the Dirichlet and Neumann boundary conditions. The instantaneous dynamic equation for variations in temperature, which specifies the entropy mode, is solved analytically for some types of acoustic exciters. The results show variation in temperature as a function of time and distance from the boundary for different boundary conditions.
4
Content available Asymptotic profiles for a class of perturbed burgers equations in one space dimension
Dkhil F., Hamza M. A., Mannoubi B.
Opuscula Mathematica
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2018
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Vol. 38, no. 1
41--80
EN
In this article we consider the Burgers equation with some class of perturbations in one space dimension. Using various energy lunctionals in appropriate weighted Sobolev spaces rewritten in the variables [formula] and log τ, we prove that the large time behavior of solutions is given by the sell-similar solutions ol the associated Burgers equation.
5
Content available Rigorous Integration of Burgers Equation
Cyranka J.
Challenges of Modern Technology
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2011
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Vol. 2, no. 3
3--7
EN
This paper presents techniques that allows to rigorously integrate dissipative partial differential equations. A full case study of an application to the Burgers equation on the line with periodic boundary conditions is presented.
6
Content available Modeling of the finite amplitude plane wave propagation in non-dissipative medium
Baranowska A.
Hydroacoustics
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2008
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Vol. 11
11-18
EN
The paper presents results of theoretical analysis of the finite amplitude plane wave propagation problem. The case of harmonic plane wave propagation in non-dissipative medium was considered. The mathematical model and some results of numerical investigations are presented. The mathematical model was built on the basis of one-dimensional continuity equation, equation of motion in differential form and state equation. The finite difference method was applied to solve the problem numerically. The pressure changes and harmonic pressure amplitude changes were analysed. The results of computer calculations were compared with solution of the Burgers equation.
7
Content available remote Modelling of acoustic heating induced by different types of sound
Perelomova A.
Archives of Acoustics
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2008
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Vol. 33, No. 2
209-219
EN
Dynamic equation governing acoustic heating is derived by splitting of the conservation laws into acoustic and non-acoustic parts. Numerical simulations result in the general conclusions about efficiency of acoustic heating produced by pulses of different polarity and shape. Efficiency of heating induced by stochastic and regular periodic sound of the identical intensity is numerically investigated.
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