用Symbolic Computation计算毛细重力波六阶解

本文首先运用Symbolic Computation在半物理平面(x,)上计算了毛细重力波的六阶解,得到了波形与色散关系,低阶解与 Hogan 结果一致。

Computation of turbulent-flow in a square duct - aspects of the secondary flow and its origin

A numerical study of turbulent flow in a straight duct of square cross-section is made. An order-of-magnitude analysis of the 3-D, time-averaged Navier-Stokes equations resulted in a parabolic form of the Navier-Stokes equations. The governing equations, expressed in terms of a new vector-potential formulation, are expanded as a multi-deck structure with each deck characterized by its dominant physical forces. The resulting equations are solved using a finite-element approach with a bicubic element representation on each cross-sectional plane. The numerical integration along the streamwise direction is carried out with finite-difference approximations until a fully-developed state is reached. The computed results agree well with other numerical studies and compare very favorably with the available experimental data. One important outcome of the current investigation is the interpretation analytically that the driving force of the secondary flow in a square duct comes mainly from the second-order terms of the difference in the gradients of the normal and transverse Reynolds stresses in the axial vorticity equation.

Computation of turbulence-generated noise by large-eddy simulation

The hybrid method of large eddy simulation (LES) and the Lighthill analogy is being developed to compute the sound radiated from turbulent flows. The results obtained from the hybrid method are often contaminated by the absence of small scales in LES, since the energy level of sound is much smaller than that of turbulent flows. Previous researches investigate the effects of subgrid sacle (SGS) eddies on the frequency spectra of sound radiated by isotropic turbulence and suggest a SGS noise model to represent the SGS contributions to the frequency spectra. Their investigations are conducted in physical space and are unavoidably influenced by boundary conditions. In this paper, we propose to perform such calculations in Fourier space so that the effects of boundary conditions can be correctly treated. Posteriori tests are carried out to investigate the SGS contribution to the sound. The results obtained recover the -7/2 law within certain wave-number ranges, but under-estimate the amplitudes of the frequency spectra. The reason for the underestimation is also discussed.

Computation of flow over a rotating body on unstructured Chimera mesh

Flow around moving boundary is ubiquitous in engineering applications. To increse the efficienly of the algorithm to handle moving boundaries is still a major challenge in Computational Fluid Dynamics (CFD). The Chimera grid method is one type of method to handle moving boundaries. A concept of domain de-composition has been proposed in this paper. In this method, sub-domains are meshed independently and governing equations are also solved separately on them. The Chimera grid method was originally used only on structured (curvilinear) meshes. However, in a problem which involves both moving boundary and complex geometry, the number of sub-domains required in a traditional (structured) Chimera method becomes fairly large. Thus the time required in the interior boundary locating, link-building and data exchanging also increases. The use of unstructured Chimera grid can reduce the time consumption significantly by the reduction of domain(block) number. Generally speaking, unstructured Chimera grid method has not been developed. In this paper, a well-known pressure correction scheme - SIMPLEC is modified and implemented on unstructured Chimera mesh. A new interpolation scheme regarding the pressure correction is proposed to prevent the possible decoupling of pressure. A moving-mesh finite volume approach is implemented in an inertial reference frame. This approach is then used to compute incompressible flow around a rotating circular and elliptic cylinder. These numerical examples demonstrate the capability of the proposed scheme in handling moving boundaries. The numerical results are in good agreement with other experimental and computational data in literature. The method proposed in this paper can be efficiently applied to more challenge cases such as free-falling objects or heavy particles in fluid.