-According to basic equations of fluid mechanics, this paper presents a unified variational principle of fluid mechanics (UVPFM) by using the optimization method of weighted residuals (OMWR). The advantages are as fol...-According to basic equations of fluid mechanics, this paper presents a unified variational principle of fluid mechanics (UVPFM) by using the optimization method of weighted residuals (OMWR). The advantages are as follows, the establishment of the functional and the variational principle is easy, it can change various problems of fluid mechanics derived by basic equations into a unified optimization problem, and the solution is the optimum one in some sense. According to the OMWR for the solitary subdomain, this paper uses UVPFM onto any solitary subdomain and gives the solution of the hydrodynamics equation which is suitable only for that solitary subdomain. According to the OMWR for solitary point, this paper uses UVPFM to any solitary point and gives the solution of the hydrodynamics equation (point solution) which is suitable only for that solitary point. As the solution for the solitary subdomain or solitary point is developed independently, the compatibility with other subdomain or other points, does not need to be considered, but all the boundary conditions and the supplementary derived residual equations obtained by running the derivative operations to the differential equation should be taken into account.展开更多
In this paper, the variational principles of hydrodynamic problems for the incompressible and compressible viscous fluids are established. These principles are principles of maximum power losses. Their generalized var...In this paper, the variational principles of hydrodynamic problems for the incompressible and compressible viscous fluids are established. These principles are principles of maximum power losses. Their generalized variational principles are also discussed on the basis of Lagrangian multiplier methods.展开更多
This paper summarized the recent development on Herglotz’s generalized variational principle and its symmetries and conserved quantities for nonconservative dynamical systems.Taking Lagrangian mechanics,Hamiltonian m...This paper summarized the recent development on Herglotz’s generalized variational principle and its symmetries and conserved quantities for nonconservative dynamical systems.Taking Lagrangian mechanics,Hamiltonian mechanics and Birkhoffian mechanics as three research frames,we introduce Herglotz’s generalized variational principle,dynamical equations of Herglotz type,Noether symmetry and conserved quantities,and their generalization to time-delay dynamics,fractional dynamics and time-scale dynamics,and put forward some problems as suggestions for future research.展开更多
The generalized variational principles of isothermal quasi-static fluid full-filled elastic solids are established by using Variational Integral Method. Then by introducing constraints, several kinds of variational pr...The generalized variational principles of isothermal quasi-static fluid full-filled elastic solids are established by using Variational Integral Method. Then by introducing constraints, several kinds of variational principles are worked out, including five-field variable, four-field variable, three-field variable and two-field variable formulations. Some new variational principles are presented besides the principles noted in the previous works. Based on variational principles, finite element models can be set up.展开更多
Based on the author’s previous work, a general form of generalized variational princi-ples (VPs) together with its derived VP family is established for 3-D unsteady’ transonicpotential flow with shocks past arbitrar...Based on the author’s previous work, a general form of generalized variational princi-ples (VPs) together with its derived VP family is established for 3-D unsteady’ transonicpotential flow with shocks past arbitrary wings oscillating periodically. To facilitate thenumerical handling, full use is made of functional variations with variable domain and natu-ral boundary conditions (BC) so that almost all boundary/interface conditions, including theRankine-Hugoniot shock relations and slip conditions across free trailing vortex sheets, havebeen converted into natural ones. Also distributed suction/blowing along the wing surfacefor the boundary layer control is accounted for. This theory aims at rendering a general,rigorous theoretical basis for the finite element metbod and other direct variational methods,and it can be generalized to both wing-body combinations and 3-D rotating bladings, includ-ing the subsonic flow as a special case.展开更多
文摘-According to basic equations of fluid mechanics, this paper presents a unified variational principle of fluid mechanics (UVPFM) by using the optimization method of weighted residuals (OMWR). The advantages are as follows, the establishment of the functional and the variational principle is easy, it can change various problems of fluid mechanics derived by basic equations into a unified optimization problem, and the solution is the optimum one in some sense. According to the OMWR for the solitary subdomain, this paper uses UVPFM onto any solitary subdomain and gives the solution of the hydrodynamics equation which is suitable only for that solitary subdomain. According to the OMWR for solitary point, this paper uses UVPFM to any solitary point and gives the solution of the hydrodynamics equation (point solution) which is suitable only for that solitary point. As the solution for the solitary subdomain or solitary point is developed independently, the compatibility with other subdomain or other points, does not need to be considered, but all the boundary conditions and the supplementary derived residual equations obtained by running the derivative operations to the differential equation should be taken into account.
文摘In this paper, the variational principles of hydrodynamic problems for the incompressible and compressible viscous fluids are established. These principles are principles of maximum power losses. Their generalized variational principles are also discussed on the basis of Lagrangian multiplier methods.
基金supported by the National Natural Science Foundations of China (Nos. 11972241,11572212,11272227)the Natural Science Foundation of Jiangsu Province(No. BK20191454).
文摘This paper summarized the recent development on Herglotz’s generalized variational principle and its symmetries and conserved quantities for nonconservative dynamical systems.Taking Lagrangian mechanics,Hamiltonian mechanics and Birkhoffian mechanics as three research frames,we introduce Herglotz’s generalized variational principle,dynamical equations of Herglotz type,Noether symmetry and conserved quantities,and their generalization to time-delay dynamics,fractional dynamics and time-scale dynamics,and put forward some problems as suggestions for future research.
文摘The generalized variational principles of isothermal quasi-static fluid full-filled elastic solids are established by using Variational Integral Method. Then by introducing constraints, several kinds of variational principles are worked out, including five-field variable, four-field variable, three-field variable and two-field variable formulations. Some new variational principles are presented besides the principles noted in the previous works. Based on variational principles, finite element models can be set up.
文摘Based on the author’s previous work, a general form of generalized variational princi-ples (VPs) together with its derived VP family is established for 3-D unsteady’ transonicpotential flow with shocks past arbitrary wings oscillating periodically. To facilitate thenumerical handling, full use is made of functional variations with variable domain and natu-ral boundary conditions (BC) so that almost all boundary/interface conditions, including theRankine-Hugoniot shock relations and slip conditions across free trailing vortex sheets, havebeen converted into natural ones. Also distributed suction/blowing along the wing surfacefor the boundary layer control is accounted for. This theory aims at rendering a general,rigorous theoretical basis for the finite element metbod and other direct variational methods,and it can be generalized to both wing-body combinations and 3-D rotating bladings, includ-ing the subsonic flow as a special case.
