Conditional nonlinear optimal perturbation(CNOP) is an extension of the linear singular vector technique in the nonlinear regime.It represents the initial perturbation that is subjected to a given physical constraint,...Conditional nonlinear optimal perturbation(CNOP) is an extension of the linear singular vector technique in the nonlinear regime.It represents the initial perturbation that is subjected to a given physical constraint,and results in the largest nonlinear evolution at the prediction time.CNOP-type errors play an important role in the predictability of weather and climate.Generally,when calculating CNOP in a complicated numerical model,we need the gradient of the objective function with respect to the initial perturbations to provide the descent direction for searching the phase space.The adjoint technique is widely used to calculate the gradient of the objective function.However,it is difficult and cumbersome to construct the adjoint model of a complicated numerical model,which imposes a limitation on the application of CNOP.Based on previous research,this study proposes a new ensemble projection algorithm based on singular vector decomposition(SVD).The new algorithm avoids the localization procedure of previous ensemble projection algorithms,and overcomes the uncertainty caused by choosing the localization radius empirically.The new algorithm is applied to calculate the CNOP in an intermediate forecasting model.The results show that the CNOP obtained by the new ensemble-based algorithm can effectively approximate that calculated by the adjoint algorithm,and retains the general spatial characteristics of the latter.Hence,the new SVD-based ensemble projection algorithm proposed in this study is an effective method of approximating the CNOP.展开更多
Based on the idea of adjoint method and the dynamic evolution method,a new optimum aerodynamic design technique is presented in this paper.It can be applied to the optimum problems with a large number of design variab...Based on the idea of adjoint method and the dynamic evolution method,a new optimum aerodynamic design technique is presented in this paper.It can be applied to the optimum problems with a large number of design variables and is time saving.The key of the new method lies in that the optimization process is regarded as an unsteady evolution,i.e.,the optimization is executed,simultaneously with solving the unsteady flow governing equations and adjoint equations.Numerical examples for both the inverse problem and drag minimization using Euler equations have been presented,and the results show that the method presented in this paper is more efficient than the optimum methods based on the steady flow solution and the steady solution of adjoint equations.展开更多
基金jointly sponsored by the National Natural Science Foundation of China(Grant Nos.41176013,41230420 and 41006007)
文摘Conditional nonlinear optimal perturbation(CNOP) is an extension of the linear singular vector technique in the nonlinear regime.It represents the initial perturbation that is subjected to a given physical constraint,and results in the largest nonlinear evolution at the prediction time.CNOP-type errors play an important role in the predictability of weather and climate.Generally,when calculating CNOP in a complicated numerical model,we need the gradient of the objective function with respect to the initial perturbations to provide the descent direction for searching the phase space.The adjoint technique is widely used to calculate the gradient of the objective function.However,it is difficult and cumbersome to construct the adjoint model of a complicated numerical model,which imposes a limitation on the application of CNOP.Based on previous research,this study proposes a new ensemble projection algorithm based on singular vector decomposition(SVD).The new algorithm avoids the localization procedure of previous ensemble projection algorithms,and overcomes the uncertainty caused by choosing the localization radius empirically.The new algorithm is applied to calculate the CNOP in an intermediate forecasting model.The results show that the CNOP obtained by the new ensemble-based algorithm can effectively approximate that calculated by the adjoint algorithm,and retains the general spatial characteristics of the latter.Hence,the new SVD-based ensemble projection algorithm proposed in this study is an effective method of approximating the CNOP.
文摘Based on the idea of adjoint method and the dynamic evolution method,a new optimum aerodynamic design technique is presented in this paper.It can be applied to the optimum problems with a large number of design variables and is time saving.The key of the new method lies in that the optimization process is regarded as an unsteady evolution,i.e.,the optimization is executed,simultaneously with solving the unsteady flow governing equations and adjoint equations.Numerical examples for both the inverse problem and drag minimization using Euler equations have been presented,and the results show that the method presented in this paper is more efficient than the optimum methods based on the steady flow solution and the steady solution of adjoint equations.
