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GENERAL VARIATIONAL PRINCIPLE FAMILY FOR FULLY 3-D UNSTEADY TRANSONIC FLOW WITH SHOCKS AROUND OSCILLATING WINGS

GENERAL VARIATIONAL PRINCIPLE FAMILY FOR FULLY 3-D UNSTEADY TRANSONIC FLOW WITH SHOCKS AROUND OSCILLATING WINGS
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摘要 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. 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.
作者 刘高联
出处 《Science China Mathematics》 SCIE 1989年第6期707-715,共9页 中国科学:数学(英文版)
关键词 variational principles in fluid mechanics UNSTEADY FLOW finite element method TRANSONIC flow. variational principles in fluid mechanics unsteady flow finite element method transonic flow.
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