We show existence of time-periodic supersonic solutions in a finite interval, after certain start-up time depending on the length of the interval, to the one space-dimensional isentropic compressible Euler equations, ...We show existence of time-periodic supersonic solutions in a finite interval, after certain start-up time depending on the length of the interval, to the one space-dimensional isentropic compressible Euler equations, subjected to periodic boundary conditions. Both classical solutions and weak entropy solutions, as well as high-frequency limiting behavior are considered. The proofs depend on the theory of Cauchy problems of genuinely nonlinear hyperbolic systems of conservation laws.展开更多
The work presented here shows the unsteady inviscid results obtained for the twoand three-dimensional wings which are in rigid and flexible osciliations.The results are generated by a finite volume Euler method. It ...The work presented here shows the unsteady inviscid results obtained for the twoand three-dimensional wings which are in rigid and flexible osciliations.The results are generated by a finite volume Euler method. It is based on theRunge- Kutta time stepping scheme developed by Jameson et al.. To increase the timestep which is limited by the stability of Runge-Kutta scheme, the implicit residualsmoothing which is modified by using variable coefficients io prerent the loss of flowphysics for the unsteady flows is engaged in the calculations. With this unconditionalstable solver the unsteady flws about the wings in arbitrary motion can be receivedefficiently.The two- and three-dimensional rectangular wings which are in rigid andflexible pitching oscillations in the transonic flow are invesigated here, some of thecomputational results are compared with the experimental data. The influence of thereduced frequency for the two kinds of the wings are researched. All the results givenin this work are reasonable.展开更多
A high-order accurate explicit scheme is proposed for solving Euler/Reynolds-averaged Navier-Stokes equations for steady and unsteady flows, respectively. Baldwin-Lomax turbulence model is utilized to obtain the turbu...A high-order accurate explicit scheme is proposed for solving Euler/Reynolds-averaged Navier-Stokes equations for steady and unsteady flows, respectively. Baldwin-Lomax turbulence model is utilized to obtain the turbulent viscosity. For the explicit scheme, the Runge-Kutta time-stepping methods of third orders are used in time integration, and space discretization for the right-hand side (RHS) terms of semi-discrete equations is performed by third-order ENN scheme for inviscid terms and fourth-order compact difference for viscous terms. Numerical experiments suggest that the present scheme not only has a fairly rapid convergence rate, but also can generate a highly resolved approximation to numerical solution, even to unsteady problem.展开更多
基金supported by the National Natural Science Foundation of China(11371141 and 11871218)Science and Technology Commission of Shanghai Municipality(STCSM)under Grant No.18dz2271000
文摘We show existence of time-periodic supersonic solutions in a finite interval, after certain start-up time depending on the length of the interval, to the one space-dimensional isentropic compressible Euler equations, subjected to periodic boundary conditions. Both classical solutions and weak entropy solutions, as well as high-frequency limiting behavior are considered. The proofs depend on the theory of Cauchy problems of genuinely nonlinear hyperbolic systems of conservation laws.
文摘The work presented here shows the unsteady inviscid results obtained for the twoand three-dimensional wings which are in rigid and flexible osciliations.The results are generated by a finite volume Euler method. It is based on theRunge- Kutta time stepping scheme developed by Jameson et al.. To increase the timestep which is limited by the stability of Runge-Kutta scheme, the implicit residualsmoothing which is modified by using variable coefficients io prerent the loss of flowphysics for the unsteady flows is engaged in the calculations. With this unconditionalstable solver the unsteady flws about the wings in arbitrary motion can be receivedefficiently.The two- and three-dimensional rectangular wings which are in rigid andflexible pitching oscillations in the transonic flow are invesigated here, some of thecomputational results are compared with the experimental data. The influence of thereduced frequency for the two kinds of the wings are researched. All the results givenin this work are reasonable.
基金The project supported by the National Natural Science Foundation of China under Contract No.59576007 and 19572038
文摘A high-order accurate explicit scheme is proposed for solving Euler/Reynolds-averaged Navier-Stokes equations for steady and unsteady flows, respectively. Baldwin-Lomax turbulence model is utilized to obtain the turbulent viscosity. For the explicit scheme, the Runge-Kutta time-stepping methods of third orders are used in time integration, and space discretization for the right-hand side (RHS) terms of semi-discrete equations is performed by third-order ENN scheme for inviscid terms and fourth-order compact difference for viscous terms. Numerical experiments suggest that the present scheme not only has a fairly rapid convergence rate, but also can generate a highly resolved approximation to numerical solution, even to unsteady problem.
