It is showed that, as the Mach number goes to zero, the weak solution of the compressible Navier-Stokes equations in the whole space with general initial data converges to the strong solution of the incompressible Nav...It is showed that, as the Mach number goes to zero, the weak solution of the compressible Navier-Stokes equations in the whole space with general initial data converges to the strong solution of the incompressible Navier-Stokes equations as long as the later exists. The proof of the result relies on the new modulated energy functional and the Strichartz's estimate of linear wave equation.展开更多
In this paper,we calculated the spatial local-averaged velocity strains along the streamwise direction at four spatial scales according to the concept of spatial local-averaged velocity structure function by using the...In this paper,we calculated the spatial local-averaged velocity strains along the streamwise direction at four spatial scales according to the concept of spatial local-averaged velocity structure function by using the three-dimensional three-component database of time series of velocity vector field in the turbulent boundary layer measured by tomographic time-resolved particle image velocimetry.An improved quadrant splitting method,based on the spatial local-averaged velocity strains together with a new conditional sampling phase average technique,was introduced as a criterion to detect the coherent structure topology.Furthermore,we used them to detect and extract the spatial topologies of fluctuating velocity and fluctuating vorticity whose center is a strong second-quadrant event(Q2) or a fourth-quadrant event(Q4).Results illustrate that a closer similarity of the multi-scale coherent structures is present in the wall-normal direction,compared to the one in the other two directions.The relationship among such topological coherent structures and Reynolds stress bursting events,as well as the fluctuating vorticity was discussed.When other burst events are surveyed(the first-quadrant event Q1 and the third-quadrant event Q3),a fascinating bursting period circularly occurs:Q4-S-Q2-Q3-Q2-Q1-Q4-S-Q2-Q3-Q2-Q1 in the center of such topological structures along the streamwise direction.In addition,the probability of the Q2 bursting event occurrence is slightly higher than that of the Q4 event occurrence.The spatial instable singularity that almost simultaneously appears together with typical Q2 or Q4 events has been observed,which is the main character of the mutual induction mechanism and vortex auto-generation mechanism explaining how the turbulence is produced and maintained.展开更多
This paper establishes a new finite volume element scheme for Poisson equation on trian- gular meshes. The trial function space is taken as Lagrangian cubic finite element space on triangular partition, and the test f...This paper establishes a new finite volume element scheme for Poisson equation on trian- gular meshes. The trial function space is taken as Lagrangian cubic finite element space on triangular partition, and the test function space is defined as piecewise constant space on dual partition. Under some weak condition about the triangular meshes, the authors prove that the stiffness matrix is uni- formly positive definite and convergence rate to be O（h3） in Hi-norm. Some numerical experiments confirm the theoretical considerations.展开更多
基金supported by the National Natural Science Foundation of China (Nos. 10431060, 10701011,10501047) the Nanjing University Talent Development Foundation
文摘It is showed that, as the Mach number goes to zero, the weak solution of the compressible Navier-Stokes equations in the whole space with general initial data converges to the strong solution of the incompressible Navier-Stokes equations as long as the later exists. The proof of the result relies on the new modulated energy functional and the Strichartz's estimate of linear wave equation.
基金supported by the National Basic Research Program of China(Grant No.2012CB720101)the National Natural Science Foundation of China(Grant No.10832001)the Opening Subject of State Key Laboratory of Nonlinear Mechanics,Institute of Mechanics,Chinese Academy of Sciences
文摘In this paper,we calculated the spatial local-averaged velocity strains along the streamwise direction at four spatial scales according to the concept of spatial local-averaged velocity structure function by using the three-dimensional three-component database of time series of velocity vector field in the turbulent boundary layer measured by tomographic time-resolved particle image velocimetry.An improved quadrant splitting method,based on the spatial local-averaged velocity strains together with a new conditional sampling phase average technique,was introduced as a criterion to detect the coherent structure topology.Furthermore,we used them to detect and extract the spatial topologies of fluctuating velocity and fluctuating vorticity whose center is a strong second-quadrant event(Q2) or a fourth-quadrant event(Q4).Results illustrate that a closer similarity of the multi-scale coherent structures is present in the wall-normal direction,compared to the one in the other two directions.The relationship among such topological coherent structures and Reynolds stress bursting events,as well as the fluctuating vorticity was discussed.When other burst events are surveyed(the first-quadrant event Q1 and the third-quadrant event Q3),a fascinating bursting period circularly occurs:Q4-S-Q2-Q3-Q2-Q1-Q4-S-Q2-Q3-Q2-Q1 in the center of such topological structures along the streamwise direction.In addition,the probability of the Q2 bursting event occurrence is slightly higher than that of the Q4 event occurrence.The spatial instable singularity that almost simultaneously appears together with typical Q2 or Q4 events has been observed,which is the main character of the mutual induction mechanism and vortex auto-generation mechanism explaining how the turbulence is produced and maintained.
基金This research is supported by the ＇985＇ programme of Jilin University, the National Natural Science Foundation of China under Grant Nos. 10971082 and 11076014.
文摘This paper establishes a new finite volume element scheme for Poisson equation on trian- gular meshes. The trial function space is taken as Lagrangian cubic finite element space on triangular partition, and the test function space is defined as piecewise constant space on dual partition. Under some weak condition about the triangular meshes, the authors prove that the stiffness matrix is uni- formly positive definite and convergence rate to be O（h3） in Hi-norm. Some numerical experiments confirm the theoretical considerations.
