This article aims at studying one dimensional unsteady planar and cylindrically symmetric flow involving shocks under the influence of magnetic field. The method of generalized wavefront expansion (GWE) is employed to...This article aims at studying one dimensional unsteady planar and cylindrically symmetric flow involving shocks under the influence of magnetic field. The method of generalized wavefront expansion (GWE) is employed to derive a coupled system of nonlinear transport equations for the jump of field variables and of its spatial derivatives across the shock, which, in turn determine the evolution of wave amplitude and admit a solution that agrees with the classical decay laws of weak shocks. A closed form solution exhibiting the features of nonlinear steepening of the wave front. A general criterion for a compression wave to steepen into a shock is derived. An analytic expression elucidating how the shock formation distance is influenced by the magnetic field strength is obtained. Also, the effects of geometrical spreading and nonlinear convection on the distortion of the waveform are investigated in the presence of magnetic field.展开更多
We investigate the elementary wave interactions for the simplified combustion model in magnetogasdynamics. Under the modified entropy conditions, we construct the unique solution and observe some interesting phenomena...We investigate the elementary wave interactions for the simplified combustion model in magnetogasdynamics. Under the modified entropy conditions, we construct the unique solution and observe some interesting phenomena;such as, the combustion wave may be extinguished by the contact discontinuity or the shock wave. Especially, the transition between the detonation wave and the deflagration wave is also captured.展开更多
文摘This article aims at studying one dimensional unsteady planar and cylindrically symmetric flow involving shocks under the influence of magnetic field. The method of generalized wavefront expansion (GWE) is employed to derive a coupled system of nonlinear transport equations for the jump of field variables and of its spatial derivatives across the shock, which, in turn determine the evolution of wave amplitude and admit a solution that agrees with the classical decay laws of weak shocks. A closed form solution exhibiting the features of nonlinear steepening of the wave front. A general criterion for a compression wave to steepen into a shock is derived. An analytic expression elucidating how the shock formation distance is influenced by the magnetic field strength is obtained. Also, the effects of geometrical spreading and nonlinear convection on the distortion of the waveform are investigated in the presence of magnetic field.
文摘We investigate the elementary wave interactions for the simplified combustion model in magnetogasdynamics. Under the modified entropy conditions, we construct the unique solution and observe some interesting phenomena;such as, the combustion wave may be extinguished by the contact discontinuity or the shock wave. Especially, the transition between the detonation wave and the deflagration wave is also captured.
