The flow-induced noise is simulated with a hybrid method.Firstly,a steady-state background flow field is given by solving Reynolds averaged Navier-Stokes(RANS)equations with finite volume(FV)method on structured grid....The flow-induced noise is simulated with a hybrid method.Firstly,a steady-state background flow field is given by solving Reynolds averaged Navier-Stokes(RANS)equations with finite volume(FV)method on structured grid.Then the linearized Euler equations(LEE)can be constructed based on the resulted background flow field,where the source term on the right hand side is computed using stochastic noise generation and radiation(SNGR)method.Finally,the unsteady acoustic field is obtained through solving LEE using high-order discontinuous Galerkin(DG)method on unstructured grid,where the parallel computing based on mesh partitioning and a″Quadrature-Free Implementation″method for high-order DG are employed to accelerate the computation.In order to demonstrate the sound propagation in detail,a visualization method for high-order schemes is also developed here.Moreover,in order to test the validation and the accuracy,a 3D cavity test in comparison with the experimental data is displayed first in this paper,then a 3D high-lift wing is also simulated to demonstrate its capability for very complex geometries.展开更多
Using stopping time method we proved the Φ-inequalities, pointwise convergence, strong and weak laws of large numbers of Hardy martingale transforms with values in complex Banach spaces, and applying them to give sev...Using stopping time method we proved the Φ-inequalities, pointwise convergence, strong and weak laws of large numbers of Hardy martingale transforms with values in complex Banach spaces, and applying them to give several characterizations of AUMD spaces.展开更多
基金Supported by the Aeronautical Science Foundation of China(20101552018)the National Natural Science Foundation of China(11272152)
文摘The flow-induced noise is simulated with a hybrid method.Firstly,a steady-state background flow field is given by solving Reynolds averaged Navier-Stokes(RANS)equations with finite volume(FV)method on structured grid.Then the linearized Euler equations(LEE)can be constructed based on the resulted background flow field,where the source term on the right hand side is computed using stochastic noise generation and radiation(SNGR)method.Finally,the unsteady acoustic field is obtained through solving LEE using high-order discontinuous Galerkin(DG)method on unstructured grid,where the parallel computing based on mesh partitioning and a″Quadrature-Free Implementation″method for high-order DG are employed to accelerate the computation.In order to demonstrate the sound propagation in detail,a visualization method for high-order schemes is also developed here.Moreover,in order to test the validation and the accuracy,a 3D cavity test in comparison with the experimental data is displayed first in this paper,then a 3D high-lift wing is also simulated to demonstrate its capability for very complex geometries.
文摘Using stopping time method we proved the Φ-inequalities, pointwise convergence, strong and weak laws of large numbers of Hardy martingale transforms with values in complex Banach spaces, and applying them to give several characterizations of AUMD spaces.
