An efficient direct spectral domain decomposition method is developed coupled with Chebyshev spectral approximation for the solution of 2D, unsteady and in- compressible Navier-Stokes equations in complex geometries. ...An efficient direct spectral domain decomposition method is developed coupled with Chebyshev spectral approximation for the solution of 2D, unsteady and in- compressible Navier-Stokes equations in complex geometries. In this numerical approach, the spatial domains of interest are decomposed into several non-overlapping rectangu- lar sub-domains. In each sub-domain, an improved projection scheme with second-order accuracy is used to deal with the coupling of velocity and pressure, and the Chebyshev collocation spectral method （CSM） is adopted to execute the spatial discretization. The influence matrix technique is employed to enforce the continuities of both variables and their normal derivatives between the adjacent sub-domains. The imposing of the Neu- mann boundary conditions to the Poisson equations of pressure and intermediate variable will result in the indeterminate solution. A new strategy of assuming the Dirichlet bound- ary conditions on interface and using the first-order normal derivatives as transmission conditions to keep the continuities of variables is proposed to overcome this trouble. Three test cases are used to verify the accuracy and efficiency, and the detailed comparison be- tween the numerical results and the available solutions is done. The results indicate that the present method is efficiency, stability, and accuracy.展开更多
The stability of Bickley jet with particle laden flow is investigated numerically. The stability characteristics are calculated for various Stokes numbers and particle concentrations. The results confirm the author＇s...The stability of Bickley jet with particle laden flow is investigated numerically. The stability characteristics are calculated for various Stokes numbers and particle concentrations. The results confirm the author＇s early calculations, which also shows that the numerical program is reliable. It is further shown that there is a critical value for the effect of Stokes number, which is about 2. The most damped mode occurs when Stokes number is of order of 10 for different particle concentrations and depends weakly on the wave number. The difference in the eigenfunctions and its derivatives between the particle-laden flow and the clean gas flow is insignificant for fine particles, while the difference for coarse particles is significant.展开更多
基金Project supported by the National Natural Science Foundation of China(No.51176026)the Fundamental Research Funds for the Central Universities(No.DUT14RC(3)029)
文摘An efficient direct spectral domain decomposition method is developed coupled with Chebyshev spectral approximation for the solution of 2D, unsteady and in- compressible Navier-Stokes equations in complex geometries. In this numerical approach, the spatial domains of interest are decomposed into several non-overlapping rectangu- lar sub-domains. In each sub-domain, an improved projection scheme with second-order accuracy is used to deal with the coupling of velocity and pressure, and the Chebyshev collocation spectral method （CSM） is adopted to execute the spatial discretization. The influence matrix technique is employed to enforce the continuities of both variables and their normal derivatives between the adjacent sub-domains. The imposing of the Neu- mann boundary conditions to the Poisson equations of pressure and intermediate variable will result in the indeterminate solution. A new strategy of assuming the Dirichlet bound- ary conditions on interface and using the first-order normal derivatives as transmission conditions to keep the continuities of variables is proposed to overcome this trouble. Three test cases are used to verify the accuracy and efficiency, and the detailed comparison be- tween the numerical results and the available solutions is done. The results indicate that the present method is efficiency, stability, and accuracy.
基金supported by the National Natural Science Foundation of China (Grant Nos.50806023,50721005)the Program of Introducing Talents of Discipline to Universities,(111 Program,Grant No.B06019),China
文摘The stability of Bickley jet with particle laden flow is investigated numerically. The stability characteristics are calculated for various Stokes numbers and particle concentrations. The results confirm the author＇s early calculations, which also shows that the numerical program is reliable. It is further shown that there is a critical value for the effect of Stokes number, which is about 2. The most damped mode occurs when Stokes number is of order of 10 for different particle concentrations and depends weakly on the wave number. The difference in the eigenfunctions and its derivatives between the particle-laden flow and the clean gas flow is insignificant for fine particles, while the difference for coarse particles is significant.
