In this paper, the Crank-Nicholson + component-consistent pressure correction method for the numerical solution of the unsteady incompressible Navier-Stokes equation of [1] on the rectangular half-Staggered mesh has b...In this paper, the Crank-Nicholson + component-consistent pressure correction method for the numerical solution of the unsteady incompressible Navier-Stokes equation of [1] on the rectangular half-Staggered mesh has been extended to the curvilinear half-Staggered mesh. The discrete projection, both for the projection step in the solution procedure and for the related differential-algebraic equations, has been carefully studied and verified. It is proved that the proposed method is also unconditionally (in t) nonlinearly stable on the curvilinear mesh, provided the mesh is not too skewed. It is seen that for problems with an outflow boundary, the half-Staggered mesh is especially advantageous. Results of preliminary numerical experiments support these claims.展开更多
The authors discuss the dual relation of nearly very convexity and property WS. By two kinds of near convexities and two kinds of near smoothness, the authors prove a series of characteriza- tions such that every half...The authors discuss the dual relation of nearly very convexity and property WS. By two kinds of near convexities and two kinds of near smoothness, the authors prove a series of characteriza- tions such that every half-space in Banach space X and every weak^＊ half-space in the dual space X^＊ are approximatively weakly compact and approximatively compact. They show a sufficient condition such that a Banach space X is a Asplund space. Using upper semi-continuity of duality mapping, the authors also give two characterizations of property WS and property S.展开更多
基金Supported by Projects 19472068 and 19772056 of the National Natural Science Foundation ofChina and the Laboratory of Scientifi
文摘In this paper, the Crank-Nicholson + component-consistent pressure correction method for the numerical solution of the unsteady incompressible Navier-Stokes equation of [1] on the rectangular half-Staggered mesh has been extended to the curvilinear half-Staggered mesh. The discrete projection, both for the projection step in the solution procedure and for the related differential-algebraic equations, has been carefully studied and verified. It is proved that the proposed method is also unconditionally (in t) nonlinearly stable on the curvilinear mesh, provided the mesh is not too skewed. It is seen that for problems with an outflow boundary, the half-Staggered mesh is especially advantageous. Results of preliminary numerical experiments support these claims.
基金supported by National Natural Science Foundation of China(Grant No.11271248)supported by National Natural Science Foundation of China(Grant No.11401370)
文摘The authors discuss the dual relation of nearly very convexity and property WS. By two kinds of near convexities and two kinds of near smoothness, the authors prove a series of characteriza- tions such that every half-space in Banach space X and every weak^＊ half-space in the dual space X^＊ are approximatively weakly compact and approximatively compact. They show a sufficient condition such that a Banach space X is a Asplund space. Using upper semi-continuity of duality mapping, the authors also give two characterizations of property WS and property S.
