This paper presents, an efficient approach for solving Euler-Lagrange Equation which arises from calculus of variations. Homotopy analysis method to find an approximate solution of variational problems is proposed. An...This paper presents, an efficient approach for solving Euler-Lagrange Equation which arises from calculus of variations. Homotopy analysis method to find an approximate solution of variational problems is proposed. An optimal value of the convergence control parameter is given through the square residual error. By minimizing the the square residual error, the optimal convergence-control parameters can be obtained. It is showed that the homotopy analysis method was valid and feasible to the study of variational problems.展开更多
Unsteady cavitating flow often contains vapor structures with a wide range of different length scales,from micro-bubbles to large cavities,which issues a big challenge to precisely investigate its evolution mechanism ...Unsteady cavitating flow often contains vapor structures with a wide range of different length scales,from micro-bubbles to large cavities,which issues a big challenge to precisely investigate its evolution mechanism by computational fluid dynamics(CFD)method.The present work reviews the development of simulation methods for cavitation,especially the emerging Euler-Lagrange approach.Additionally,the progress of the numerical investigation of hot and vital issues is discussed,including cavitation inception,cloud cavitation inner structure and its formation mechanism,cavitation erosion,and cavitation noise.It is indicated that the Euler-Lagrange method can determine cavitation inception point better.For cloud cavitation,the Euler-Lagrange method can reveal the source of microbubbles and their distribution law inside the shedding cloud.This method also has advantages and great potential in assessing cloud cavitation-induced erosion and noise.With the ever-growing demands of cavitation simulation accuracy in basic research and engineering applications,how to improve the Euler-Lagrange method’s stability and applicability is still an open problem.To further promote the application of this advanced CFD simulation technology in cavitation research,some key issues are to be solved and feasible suggestions are put forward for further work.展开更多
文摘This paper presents, an efficient approach for solving Euler-Lagrange Equation which arises from calculus of variations. Homotopy analysis method to find an approximate solution of variational problems is proposed. An optimal value of the convergence control parameter is given through the square residual error. By minimizing the the square residual error, the optimal convergence-control parameters can be obtained. It is showed that the homotopy analysis method was valid and feasible to the study of variational problems.
基金supported by the National Natural Science Foundation of China(Grant Nos.52176041,12102308).
文摘Unsteady cavitating flow often contains vapor structures with a wide range of different length scales,from micro-bubbles to large cavities,which issues a big challenge to precisely investigate its evolution mechanism by computational fluid dynamics(CFD)method.The present work reviews the development of simulation methods for cavitation,especially the emerging Euler-Lagrange approach.Additionally,the progress of the numerical investigation of hot and vital issues is discussed,including cavitation inception,cloud cavitation inner structure and its formation mechanism,cavitation erosion,and cavitation noise.It is indicated that the Euler-Lagrange method can determine cavitation inception point better.For cloud cavitation,the Euler-Lagrange method can reveal the source of microbubbles and their distribution law inside the shedding cloud.This method also has advantages and great potential in assessing cloud cavitation-induced erosion and noise.With the ever-growing demands of cavitation simulation accuracy in basic research and engineering applications,how to improve the Euler-Lagrange method’s stability and applicability is still an open problem.To further promote the application of this advanced CFD simulation technology in cavitation research,some key issues are to be solved and feasible suggestions are put forward for further work.
