The authors propose a dwindling filter algorithm with Zhou's modified subproblem for nonlinear inequality constrained optimization.The feasibility restoration phase,which is always used in the traditional filter m...The authors propose a dwindling filter algorithm with Zhou's modified subproblem for nonlinear inequality constrained optimization.The feasibility restoration phase,which is always used in the traditional filter method,is not needed.Under mild conditions,global convergence and local superlinear convergence rates are obtained.Numerical results demonstrate that the new algorithm is effective.展开更多
When the underexpanded supersonic jet impinges on the obstacle, it is well known that the self-induced flow os- cillation occurs. This oscillation depends on the pressure ratio in the flowfield, the position of an obs...When the underexpanded supersonic jet impinges on the obstacle, it is well known that the self-induced flow os- cillation occurs. This oscillation depends on the pressure ratio in the flowfield, the position of an obstacle and is related with the noise problems of aeronautical and other industrial engineering. The characteristic and the mechanism of self-induced flow oscillation, have to be clarified to control various noise problems. But, it seems that the characteristics of the oscillated flowfield and the mechanism of an oscillation have to be more cleared to control the oscillation. This paper aims to clarify the effect of the pressure ratio and the obstacle position and the mechanism of self-induced flow oscillation by numerical analysis and experiment, when the underexpanded su- personic jet impinges on the cylindrical body. From the result of this study, it is clear that occurrence of the self-induced flow osciUation depends on the pressure balance in the flowfield.展开更多
When an upstream steady uniform supersonic flow impinges onto a symmetric straight-sided wedge,governed by the Euler equations,there are two possible steady oblique shock configurations if the wedge angle is less than...When an upstream steady uniform supersonic flow impinges onto a symmetric straight-sided wedge,governed by the Euler equations,there are two possible steady oblique shock configurations if the wedge angle is less than the detachment angle—the steady weak shock with supersonic or subsonic downstream flow(determined by the wedge angle that is less than or greater than the sonic angle)and the steady strong shock with subsonic downstream flow,both of which satisfy the entropy condition.The fundamental issue—whether one or both of the steady weak and strong shocks are physically admissible solutions—has been vigorously debated over the past eight decades.In this paper,we survey some recent developments on the stability analysis of the steady shock solutions in both the steady and dynamic regimes.For the static stability,we first show how the stability problem can be formulated as an initial-boundary value type problem and then reformulate it into a free boundary problem when the perturbation of both the upstream steady supersonic flow and the wedge boundary are suitably regular and small,and we finally present some recent results on the static stability of the steady supersonic and transonic shocks.For the dynamic stability for potential flow,we first show how the stability problem can be formulated as an initial-boundary value problem and then use the self-similarity of the problem to reduce it into a boundary value problem and further reformulate it into a free boundary problem,and we finally survey some recent developments in solving this free boundary problem for the existence of the PrandtlMeyer configurations that tend to the steady weak supersonic or transonic oblique shock solutions as time goes to infinity.Some further developments and mathematical challenges in this direction are also discussed.展开更多
This paper proposes an inexact SQP method in association with line search filter technique for solving nonlinear equality constrained optimization. For large-scale applications, it is expensive to get an exact search ...This paper proposes an inexact SQP method in association with line search filter technique for solving nonlinear equality constrained optimization. For large-scale applications, it is expensive to get an exact search direction, and hence the authors use an inexact method that finds an approximate solution satisfying some appropriate conditions. The global convergence of the proposed algorithm is established by using line search filter technique. The second-order correction step is used to overcome the Maratos effect, while the line search filter inexact SQP method has q-superlinear local convergence rate. Finally, the results of numerical experiments indicate that the proposed method is efficient for the given test problems.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11201304,11371253)the Innovation Program of Shanghai Municipal Education Commission(No.12YZ174)the Group of Accounting and Governance Disciplines(No.10kq03)
文摘The authors propose a dwindling filter algorithm with Zhou's modified subproblem for nonlinear inequality constrained optimization.The feasibility restoration phase,which is always used in the traditional filter method,is not needed.Under mild conditions,global convergence and local superlinear convergence rates are obtained.Numerical results demonstrate that the new algorithm is effective.
文摘When the underexpanded supersonic jet impinges on the obstacle, it is well known that the self-induced flow os- cillation occurs. This oscillation depends on the pressure ratio in the flowfield, the position of an obstacle and is related with the noise problems of aeronautical and other industrial engineering. The characteristic and the mechanism of self-induced flow oscillation, have to be clarified to control various noise problems. But, it seems that the characteristics of the oscillated flowfield and the mechanism of an oscillation have to be more cleared to control the oscillation. This paper aims to clarify the effect of the pressure ratio and the obstacle position and the mechanism of self-induced flow oscillation by numerical analysis and experiment, when the underexpanded su- personic jet impinges on the cylindrical body. From the result of this study, it is clear that occurrence of the self-induced flow osciUation depends on the pressure balance in the flowfield.
基金supported by the US National Science Foundation (Grant Nos. DMS0935967 and DMS-0807551)the UK Engineering and Physical Sciences Research Council (Grant Nos. EP/E035027/1 and EP/L015811/1)+1 种基金National Natural Science Foundation of China (Grant No. 10728101)the Royal Society-Wolfson Research Merit Award (UK)
文摘When an upstream steady uniform supersonic flow impinges onto a symmetric straight-sided wedge,governed by the Euler equations,there are two possible steady oblique shock configurations if the wedge angle is less than the detachment angle—the steady weak shock with supersonic or subsonic downstream flow(determined by the wedge angle that is less than or greater than the sonic angle)and the steady strong shock with subsonic downstream flow,both of which satisfy the entropy condition.The fundamental issue—whether one or both of the steady weak and strong shocks are physically admissible solutions—has been vigorously debated over the past eight decades.In this paper,we survey some recent developments on the stability analysis of the steady shock solutions in both the steady and dynamic regimes.For the static stability,we first show how the stability problem can be formulated as an initial-boundary value type problem and then reformulate it into a free boundary problem when the perturbation of both the upstream steady supersonic flow and the wedge boundary are suitably regular and small,and we finally present some recent results on the static stability of the steady supersonic and transonic shocks.For the dynamic stability for potential flow,we first show how the stability problem can be formulated as an initial-boundary value problem and then use the self-similarity of the problem to reduce it into a boundary value problem and further reformulate it into a free boundary problem,and we finally survey some recent developments in solving this free boundary problem for the existence of the PrandtlMeyer configurations that tend to the steady weak supersonic or transonic oblique shock solutions as time goes to infinity.Some further developments and mathematical challenges in this direction are also discussed.
基金supported by the National Science Foundation Grant under Grant No.10871130the Shanghai Leading Academic Discipline Project under Grant No.T0401
文摘This paper proposes an inexact SQP method in association with line search filter technique for solving nonlinear equality constrained optimization. For large-scale applications, it is expensive to get an exact search direction, and hence the authors use an inexact method that finds an approximate solution satisfying some appropriate conditions. The global convergence of the proposed algorithm is established by using line search filter technique. The second-order correction step is used to overcome the Maratos effect, while the line search filter inexact SQP method has q-superlinear local convergence rate. Finally, the results of numerical experiments indicate that the proposed method is efficient for the given test problems.
