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  • 1
    Electronic Resource
    Electronic Resource
    Formation of cylindrical shock waves in nonequilibrium magnetogasdynamic flow (1987)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 30 (1987), S. 2194-2198 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Following Chu [in Non-Equilibrium Flows, edited by P. P. Wegener (Dekker, New York, 1970), Vol. II, p. 37], the phenomena associated with the propagation of acceleration waves in nonequilibrium magnetogasdynamic flow, which is induced by the motion of a piston advancing with finite acceleration into a constant state of rest, are studied. Also studied is the characteristic path by using the characteristics of the governing quasilinear system as the reference coordinate system. A differential equation governing the growth and decay of an acceleration wave is derived. The critical time when the breakdown of the characteristic solution occurs in the neighborhood of the leading frozen characteristic is obtained; that is, when all the characteristics will pile up at the wave front to form a shock wave. It is shown that for the slow relaxation process the effect of the magnetic field is to slow down the motion of the breakdown point along the leading frozen characteristic, and thus to increase the cylindrical shock formation time. However, the effect of the magnetic field on expansion waves is to enhance the decay rate. For the quick relaxation process, however, the effect of the magnetic field on compressive waves is to cause an early shock formation, while the effect on expansion waves is to decrease the decay rate.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.866153
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  • 2
    Electronic Resource
    Electronic Resource
    The behavior of acceleration waves in radiation magnetogasdynamic flow (1990)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 2 (1990), S. 2516-2518 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The method of characteristics is used to study the propagation of acceleration waves in a radiation magnetogasdynamic flow, which is induced by the motion of a piston advancing with a finite acceleration into a constant state of rest. The analysis assumes an azimuthal magnetic field produced by a constant current flowing along the axis. The characteristic solutions have been obtained in the neighborhood of leading forward characteristics. The critical values of the initial amplitude and critical time for breakdown of an acceleration wave at the cusp of the envelope of intersecting forward characteristics have been obtained. It has been shown that the effect of coupling of the radiation and the magnetic field on compression waves, which are emanating from piston movement, is to slow down the motion of a breakdown point, and thus to increase the cylindrical shock formation time, while the effect on expansion waves is to enhance the decay rate.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.859516
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  • 3
    Electronic Resource
    Electronic Resource
    On sonic discontinuities in an ideal radiating gas (1979)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 30 (1979), S. 937-942 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Résumé Dans cet article il s'agit de l'étude des phénomènes associés aux discontinuités soniques dans un gaz parfait rayonnant. On formule les équations différentielles gouvernant la croissance et l'amortissement de ces discontinuités. Afin de pouvoir les intégrer en toute généralité, on les transforme en une équation sur la courbe bicaractéristique dans la variété caractéristique. On donne le critère d'amortissement ou d'éclatement des discontinuités faibles. Le rayonnement contribue au développement rapide du choc.
    Notes: Abstract Following Elcrat the phenomena associated with the sonic discontinuities in an ideal radiating gas are studied here. The differential equations for growth and decay of these discontinuities are formulated. In order to integrate them in full generality they are transformed to an equation along the bicharacteristic curve in the characteristic manifold. The criterion for the decay or ‘blow up’ of weak discontinuities has been given. Radiation contributes to the fast development of shock.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01590491
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  • 4
    Electronic Resource
    Electronic Resource
    On the non-uniform propagation of weak discontinuities in magnetogasdynamics (1981)
    Springer
    Archive for rational mechanics and analysis 75 (1981), S. 169-174 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00250478
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  • 5
    Electronic Resource
    Electronic Resource
    Corrigendum to “On the non-uniform propagation of weak discontinuities in magnetogasdynamics” (1982)
    Springer
    Archive for rational mechanics and analysis 78 (1982), S. 397-398 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00249589
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  • 6
    Electronic Resource
    Electronic Resource
    On the geometry of nonequilibrium magneto gasdynamic flows (1977)
    Springer
    Flow, turbulence and combustion 33 (1977), S. 259-267 
    Details
    ISSN: 1573-1987
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract After formulation of the various dynamical and kinematical relations connecting the flow quantities with the geometrical parameters of the stream line trajectories, the expressions for the tangent, principal normal and binormal vectors and the curvature and torsion of the stream line have been obtained in-terms of the velocity components, the pressure, the density, the magnetic field and the relaxation variable. This is followed by expressing the equations governing the flow in the intrinsic forms. It has been shown that the non-equilibrium character of the gas decreases the total pressure gradient along the streamlines, but the total pressure remains constant along the binormals and if the stream lines are straight lines, the trajectories of the principal normals lie on the surface of the constant total pressure. Further, the expressions for vorticity components in terms of curvature of the stream line and the velocity gradients along the stream line and their principal normals and binormals have been obtained. Finally, a class of circular helical flows have been discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00383956
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  • 7
    Electronic Resource
    Electronic Resource
    Sonic discontinuities in a relaxing gas (1979)
    Springer
    Flow, turbulence and combustion 35 (1979), S. 151-160 
    Details
    ISSN: 1573-1987
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Following Elcrat [1] the phenomena associated with the sonic discontinuities in non-equilibrium gasdynamics have been studied here. The sonic wave in non-equilibrium gaseous medium propagates with the frozen speed of sound. The magnitude of discontinuities of the first derivatives of flow quantities in the unsteady flow of relaxing gas are shown to satisfy Riccatti equations along the orthogonal trajectories of surface S(t). In order to integrate them in full generality, they are transformed to an equation along the bicharacteristic curve in the characteristic manifold $$\sum = \mathop \cup \limits_t$$ S(t). These equations have been solved completely. The criteria for decay or “blow up” of sonic discontinuities are given and the particular cases of plane and spherical waves existing in an ideal dissociative gasdynamics have been discussed. In the case of planewave for uniform propagation, it is shown that the dissociating character of the gas is to decrease the critical time. Other cases of shock formation have been studied in detail.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00382701
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  • 8
    Electronic Resource
    Electronic Resource
    Numerical solution of regularized long-wave equation (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 579-586 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A combination of the splitting method and the cubic spline technique has been used to solve a non-linear regularized long wave (RLW) equation. The accuracy and the stability of the proposed method are discussed. Then, two numerical examples are solved to illustrate the robustness of the algorithm. The results are in good agreement with the available results.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090705
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  • 9
    Electronic Resource
    Electronic Resource
    Numerical solution of coupled burgers equations in inhomogeneous form (1995)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 20 (1995), S. 1263-1271 
    Details
    ISSN: 0271-2091
    Keywords: inhomogeneous coupled Burgers equations ; operator-splitting technique ; cubic spline function ; severe/moderate gradients ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A finite difference scheme based on the operator-splitting technique with cubic spline functions is derived for solving the two-dimensional Burgers equations in ‘inhomogeneous’ form. The scheme is of first-order accuracy in time and second-order accuracy in space direction and is unconditionally stable. The numerical results are obtained with severe/moderate gradients in the initial and boundary conditions and the steady state solutions are plotted for different values of the parameters. It is concluded that the resulting scheme works very well even in the case of very severe gradient in the solution. Also, the general nature of the scheme provides a wider application in the solution of non-linear problems.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650201106
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  • 10
    Electronic Resource
    Electronic Resource
    Cubic spline technique for solution of Burgers' equation with a semi-linear boundary condition (1992)
    New York, NY [u.a.] : Wiley-Blackwell
    Communications in Applied Numerical Methods 8 (1992), S. 235-242 
    Details
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: By using the splitting-up technique and cubic spline method, numerical solutions of Burgers' equation ut = uxx + ∊uux, 0 〈 x 〈 1, t 〉 0 and u(x, 0) known, are obtained constructively by taking either of the two pairs of the semi-linear boundary conditions: (i) u(0, t) = 0, ux(1, t) = aup(1, t), t 〉 0; (ii) u(1, t) = 0, ux(0, t), = - aup(0, t), where 0 〈 p 〈 ∞. The stability analysis of the proposed method is discussed.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1630080404
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