A Galerkin spectral method based on helical-wave decomposition for the incompressible Navier–Stokes equations
文献类型：期刊论文
| 作者 | Zi-ju Liao; Wei-dong Su |
| 刊名 | International Journal for Numerical Methods in Fluids
 |
| 出版日期 | 2015 |
| 英文摘要 | This paper presents a global Galerkin spectral method for solving the incompressible Navier–Stokes equations in three-dimensional bounded domains. The method is based on helical-wave decomposition (HWD), which uses the vector eigenfunctions of the curl operator as orthogonal basis functions. We shall first review the general theory of HWD in an arbitrary simply connected domain, along with some new developments. We then employ the HWD to construct a Galerkin spectral method. The current method innovates the existing HWD-based spectral method by (a) adding a series of auxiliary fields to the HWD of the velocity field to fulfill the no-slip boundary condition and to settle the convergence problem of the HWD of the curl fields, and (b) providing a pseudo-spectral method that utilizes a fast spherical harmonic transform algorithm and Gaussian quadrature to calculate the nonlinear term in the Navier–Stokes equations. The auxiliary fields are uniquely determined by solving the Stokes and Stokes-like equations under adequate boundary conditions. The implementation of the method under the spherical geometry is presented in detail. Several numerical examples are provided to validate the proposed method. The method can be easily extended to other domains once the helical-wave bases, which depend only on the geometry of the domains, are available |
| 收录类别 | SCI |
| 原文出处 | http://onlinelibrary.wiley.com/doi/10.1002/fld.4013/full |
| 语种 | 英语 |
| 源URL | [http://ir.siat.ac.cn:8080/handle/172644/6909]  |
| 专题 | 深圳先进技术研究院_数字所 |
| 作者单位 | International Journal for Numerical Methods in Fluids |
| 推荐引用方式 GB/T 7714 | Zi-ju Liao,Wei-dong Su. A Galerkin spectral method based on helical-wave decomposition for the incompressible Navier–Stokes equations[J]. International Journal for Numerical Methods in Fluids,2015. |
| APA | Zi-ju Liao,&Wei-dong Su.(2015).A Galerkin spectral method based on helical-wave decomposition for the incompressible Navier–Stokes equations.International Journal for Numerical Methods in Fluids. |
| MLA | Zi-ju Liao,et al."A Galerkin spectral method based on helical-wave decomposition for the incompressible Navier–Stokes equations".International Journal for Numerical Methods in Fluids (2015). |
入库方式： OAI收割
来源：深圳先进技术研究院
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