We are concerned with the stability of steady multi-wave configurations for the full Euler equations of compressible fluid flow. In this paper, we focus on the stability of steady four-wave configurations that are the...We are concerned with the stability of steady multi-wave configurations for the full Euler equations of compressible fluid flow. In this paper, we focus on the stability of steady four-wave configurations that are the solutions of the Riemann problem in the flow direction, consisting of two shocks, one vortex sheet, and one entropy wave, which is one of the core multi-wave configurations for the two-dimensional Euler equations. It is proved that such steady four-wave configurations in supersonic flow are stable in structure globally, even under the BV perturbation of the incoming flow in the flow direction. In order to achieve this, we first formulate the problem as the Cauchy problem （initial value problem） in the flow direction, and then develop a modified Glimm difference scheme and identify a Glimm-type functional to obtain the required BV estimates by tracing the interactions not only between the strong shocks and weak waves, but also between the strong vortex sheet/entropy wave and weak waves. The key feature of the Euler equations is that the reflection coefficient is always less than 1, when a weak wave of different family interacts with the strong vortex sheet/entropy wave or the shock wave, which is crucial to guarantee that the Glimm functional is decreasing. Then these estimates are employed to establish the convergence of the approximate solutions to a global entropy solution, close to the background solution of steady four-wave configuration.展开更多
Firstly,the concepts of the traveling wave entropy and the feature function of traveling wave entropy were defined.Then the statistic characters of the traveling wave entropy feature function,mean value and variance w...Firstly,the concepts of the traveling wave entropy and the feature function of traveling wave entropy were defined.Then the statistic characters of the traveling wave entropy feature function,mean value and variance were analyzed after the zero-order component of the traveling wave of online cable was selected to serve as the observed object.Finally,the new recognition algorithm of minimum risk neural network was pre- sented.The simulation experiments show that the recognitions of the early fault states can be completed correctly by using the proposed recognition algorithm.The classes of cable faults include in 1-phase ground faults,and the 2-phase short circuit faults or ground faults and the 3-phase short circuit faults or ground faults,open circuit.The fault resistance range is 1×10^(-1)～1×10~9Ω.展开更多
基金supported in part by the UK Engineering and Physical Sciences Research Council Award EP/E035027/1 and EP/L015811/1
文摘We are concerned with the stability of steady multi-wave configurations for the full Euler equations of compressible fluid flow. In this paper, we focus on the stability of steady four-wave configurations that are the solutions of the Riemann problem in the flow direction, consisting of two shocks, one vortex sheet, and one entropy wave, which is one of the core multi-wave configurations for the two-dimensional Euler equations. It is proved that such steady four-wave configurations in supersonic flow are stable in structure globally, even under the BV perturbation of the incoming flow in the flow direction. In order to achieve this, we first formulate the problem as the Cauchy problem （initial value problem） in the flow direction, and then develop a modified Glimm difference scheme and identify a Glimm-type functional to obtain the required BV estimates by tracing the interactions not only between the strong shocks and weak waves, but also between the strong vortex sheet/entropy wave and weak waves. The key feature of the Euler equations is that the reflection coefficient is always less than 1, when a weak wave of different family interacts with the strong vortex sheet/entropy wave or the shock wave, which is crucial to guarantee that the Glimm functional is decreasing. Then these estimates are employed to establish the convergence of the approximate solutions to a global entropy solution, close to the background solution of steady four-wave configuration.
基金the Science and Technology Foundation of Shaanxi Province in China(2003K06G19)
文摘Firstly,the concepts of the traveling wave entropy and the feature function of traveling wave entropy were defined.Then the statistic characters of the traveling wave entropy feature function,mean value and variance were analyzed after the zero-order component of the traveling wave of online cable was selected to serve as the observed object.Finally,the new recognition algorithm of minimum risk neural network was pre- sented.The simulation experiments show that the recognitions of the early fault states can be completed correctly by using the proposed recognition algorithm.The classes of cable faults include in 1-phase ground faults,and the 2-phase short circuit faults or ground faults and the 3-phase short circuit faults or ground faults,open circuit.The fault resistance range is 1×10^(-1)～1×10~9Ω.
