Harten solution for one-dimensional unsteady equation

In order to use the second-order 5-point difference scheme mentioned to compute the solution of one dimension unsteady equations of the direct reflection of the strong plane detonation wave meeting a solid wall barrier, in this paper, we technically construct the difference schemes of the boundary and sub-boundary of the problem, and deduce the auto-analogue analytic solutions of the initial value problem, and at the same time, we present a method for the singular property of the initial value problem, from which we can get a satisfactory computation result of this difficult problem. The difference scheme used in this paper to deal with the discontinuity problems of the shock wave are valuable and worth generalization.     

An application of interacting shear flows theory: exact solution for unsteady oblique stagnation point flow

An analytical solution of the governing equations of the interacting shear flows for unsteady oblique stagnation point flow is obtained. It has the same form as that of the exact solution obtained from the complete NS equations and physical analysis and relevant discussions are then presented.The English text was polished by Yunming Chen.     

An exact solution in a nonlinear theory of rods

A three dimensional nonlinear equilibrium theory of elastic rods, applicable to large displacements and small strains, and accounting for extensibility and shear deformation is developed. Integrals of the governing equations are determined for the case of specified end force and moment. A class of solutions is obtained for an initially straight, untwisted rod and compared to the classical solution. The effects of extensibility and shear deformation are discussed.     

An exact analytical solution of the unsteady magnetohydrodynamics nonlinear dynamics of laminar boundary layer due to an impulsively linear stretching sheet

In this paper, we investigate the theoretical analysis for the unsteady magnetohydrodynamic laminar boundary layer flow due to impulsively stretching sheet. The third-order highly nonlinear partial differential equation modeling the unsteady boundary layer flow brought on by an impulsively stretching flat sheet was solved by applying Adomian decomposition method and Pade approximants. The exact analytical solution so obtained is in terms of rapidly converging power series and each of the variants are easily computable. Variations in parameters such as mass transfer (suction/injection) and Chandrasekhar number on the velocity are observed by plotting the graphs. This particular problem is technically sound and has got applications in expulsion process and related process in fluid dynamics problems.     

Numerical computation of one-dimensional unsteady flow in channels

Summary A numerical technique used in gasdynamics is here applied to the solution of one-dimensional unsteady flows in channels in the spirit of the shallow water theory. Its most important feature is the explicit treatment of imbedded bores generated in the flow by coalescence of characteristics. Four numerical examples are presented to show possible applications of the method.

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Sommario Si mostra qui l'applicazione al calcolo di correnti non stazionarie in canali, secondo la formulazione della “shallow water theory”, di metodologie numeriche già usate in gasdinamica. Il trattamento esplicito di risalti, formati per coalescenza di caratteristiche, costituisce il punto particolare del lavoro. Vengono quindi presentati quattro esempi di applicazione della metodologia numerica.

     

Appropriate boundary conditions for the solution of the equations of unsteady one-dimensional gas flow by the Lax-Wendroff method

This paper presents a new characteristic approximation to the boundary conditions, required in the solution of gas flow problems by the Law-Wendroff method. The accuracy of this and other currently used methods is assessed by a comparison with the exact solutions of two test problems     

Open-end outflow boundary approximations for the solution of the equations of unsteady one-dimensional gas flow by the Lax-Wendroff method

Open-end outflow boundary condition approximations required in the solution of gas flow problems by the Lax-Wendroff method are presented. An upwinding method is compared with that using characteristics at the boundary, and both methods are assessed by a comparison of their solutions with the theoretical solution of a test problem. The results show that the most accurate solutions may be obtained from a hybrid version of these two methods     

An unsteady MHD duct flow

An exact solution is presented for unsteady laminar flow of a viscous, incompressible, electrically conducting fluid between nonconducting, parallel, flat plates. A constant magnetic field is suddenly applied perpendicular to the plates and the motion is modified by the induced current. Numerical results are given which show how the velocity profile changes from the parabolic profile of hydrodynamics to the Hartmann profile of magnetohydrodynamics.     

An unsteady MHD duct flow

An exact solution is presented for unsteady laminar flow of a viscous, incompressible, electrically conducting fluid between nonconducting, parallel, flat plates. A constant magnetic field is suddenly applied perpendicular to the plates and the motion is modified by the induced current. Numerical results are given which show how the velocity profile changes from the parabolic profile of hydrodynamics to the Hartmann profile of magnetohydrodynamics.     

Two time scale solution for an unsteady MHD duct flow

The investigation deals with unsteady laminar flow of a viscous, incompressible, electrically conducting fluid between conducting or nonconducting flat plates. A constant magnetic field is suddenly applied perpendicular to the plates and the created electromagnetic effects modify the motion. An approximate solution is obtained using time scales t and t/ε, where ε is the small magnetic Prandtl number.     

An exact solution for thermal stresses in a three-phase composite cylinder under uniform heat flow

An exact solution is given for the stress field in a three-phase composite cylinder induced by a uniform heat flow applied at infinity. Based on the method of analytical continuation in conjunction with the alternating technique, the general expressions of the temperature and stress functions are derived explicitly in each medium of a three-phase composite cylinder. It is discovered that the stress in the inclusion is always linearly proportional to the coordinate z. Comparison is made with the special case of a two-phase composite cylinder, which shows that our results presented here are exact and general.     

An exact solution for the flow of a non-newtonian fluid past an infinite porous plate

Summary The flow of an incompressible fluid of second grade past an infinite porous plate subject to either suction or blowing at the plate is studied. It is found that existence of solutions is tied in with the sign of material moduli and in marked contrast to the Classical Newtonian, fluid solutions can be exhibited for the blowing problem.

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Sommario Si studia la corrente di un fluido incomprimibile di secondo grado che lambisce una lastra porosa da cui è succhiato o soffiato. Si trova che l'esistenza delle soluzioni è legata al segno dei moduli del materiale e, in netto contrasto col fluido newtoniano classico, si possono trovare soluzioni per il problema del soffiamento.

     

An exact analytical solution for creeping Dean flow of Bingham plastics through curved rectangular ducts

In this paper, an exact analytical solution for creeping flow of Bingham plastic fluid passing through curved rectangular ducts is presented for the first time. The closed form of axial velocity distribution, flow resistance ratio, and wall shear stress are derived using bounded Fourier transformation. An extensive investigation on mutual effects of Hedstrom number, curvature ratio, and aspect ratio is conducted. The results indicate that a drag reduction is caused in the flow field by increasing the Hedstrom number. It is shown that unlike the Newtonian creeping Dean flow, the critical aspect ratio (an aspect ratio in which the flow resistance ratio is independent from curvature ratio) does not exist at large enough Hedstrom numbers. Analytical solution also indicated that as Hedstrom number is increased, the value of Poiseuille number is enhanced, and unlike the Newtonian flows, the value of Poiseuille number is not zero at edges of cross section.     

Numerical solution of the system of one-dimensional unsteady Navier-Stokes equations for a compressible gas

In many problems encountered in modern gasdynamics, the boundary layer approximations are inadequate to account for the dissipative factors-viscosity and thermal conductivity of the gas-and the solution of the complete system of Navier-Stokes equations is required. This includes, for example, flows with large longitudinal pressure gradients, which in order of magnitude are comparable with or exceed the transverse gradients (temperature jumps, sharp flow rotations, compression shocks, etc.). In many cases, for example in flows with low density, the scale of action of the longitudinal gradients becomes significant, which leads to the need for considering the flow structure in the vicinity of the large gradients. The formulation of certain problems of this type leads to a system of one-dimensional Navier-Stokes equations.We present a difference scheme for the solution of the system of one-dimensional stationary and nonstationary Navier-Stokes equations and give examples of the calculation of the structure of the stationary shock wave front, unsteady gas flow under the influence of sudden heating of one of the boundaries, and unsteady gas flow in the vicinity of the decay of an initial discontinuity. The solution of the stationary problems is accomplished as a result of stabilization as t .The author wishes to thank V. Ya. Likhushin and V. S. Avduevskii for interest in the study and for their valuable counsel during the investigation.     

An exact nonlinear hybrid-coordinate formulation for flexible multibody systems

The previous low-order approximate nonlinear formulations succeeded in capturing the stiffening terms, but failed in simulation of mechanical systems with large deformation due to the neglect of the high-order deformation terms. In this paper, a new hybrid-coordinate formulation is proposed, which is suitable for flexible multibody systems with large deformation. On the basis of exact strain–displacement relation, equations of motion for flexible multibody system are derived by using virtual work principle. A matrix separation method is put forward to improve the efficiency of the calculation. Agreement of the present results with those obtained by absolute nodal coordinate formulation (ANCF) verifies the correctness of the proposed formulation. Furthermore, the present results are compared with those obtained by use of the linear model and the low-order approximate nonlinear model to show the suitability of the proposed models. The project supported by the National Natural Science Foundation of China (10472066, 50475021).     

Exact solution for the unsteady flow of a semi-infinite micropolar fluid

The unsteady motion of an incompressible micropolar fluid filling a half-space bounded by a horizontal infinite plate that started to move suddenly is considered. Laplace transform techniques are used. The solution in the Laplace transform domain is obtained by using a direct approach. The inverse Laplace transforms are obtained in an exact manner using the complex inversion formula of the transform together with contour integration techniques. The solution in the case of classical viscous fluids is recovered as a special case of this work when the micropolarity coecient is assumed to be zero. Numerical computations are carried out and represented graphically.     

An exact solution for the end effect of a wing of finite size in supersonic flow

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 1, pp. 65–70, January–February, 1992.     

An exact solution of the Navier-Stokes equations

Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 168–169, July–August, 1989.