A second look at the role of the fast Fourier transform as an elliptic solver
A second look at the role of the fast Fourier transform as an elliptic solver
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再看看快速傅立叶变换作为椭圆求解器的作用
DOI：
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发表时间：
2005
期刊：
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通讯作者：
E. Avital
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作者：
E. Avital
为了求解不规则和非均匀矩形交错网格上的泊松方程，将快速余弦变换(FCT)与三对角线求解器相结合。在用投影法模拟不可压缩的Navier-Stokes方程时，压力场需要这种解。对于流型边界与计算区域边界不重合的情况和非均匀网格情况，导出了一种使用FCT-三对角线求解器的新技术。该技术基于迭代过程，其中在每次迭代中求解缺陷方程，然后是松弛过程。对该方法进行了分析和数值研究，证明了该方法的解收敛于一个几何级数。进一步研究了刚体相对大小、网格拉伸、大小和纵横比对该方法的影响。新的求解器与直接数值模拟(DNS)和大涡模拟(LES)技术相结合，模拟了后向台阶和三维矩形障碍物周围的流动，得到的结果与已知结果定性地吻合得很好。版权所有©2005 John Wiley&Sons，Ltd.
A fast cosine transform (FCT) is coupled with a tridiagonal solver for the purpose of solving the Poisson equation on irregular and non‐uniform rectangular staggered grids. This kind of solution is required for the pressure field during the simulation of the incompressible Navier–Stokes equations when using the projection method. A new technique using the FCT–tridiagonal solver is derived for the cases where the boundaries of the flow regime do not coincide with the boundaries of the computational domain and for non‐uniform grids. The technique is based on an iterative procedure where a defect equation is solved in every iteration, followed by a relaxation procedure. The method is investigated analytically and numerically to show that the solution converges as a geometric series. The method is further investigated for the effects of the relative size of the rigid body, the grid stretching, size and aspect ratio. The new solver is incorporated with the direct numerical simulation (DNS) and large eddy simulation (LES) techniques to simulate the flows around a backward‐facing step and a 3D rectangular obstacle, yielding results that qualitatively compare well with known results. Copyright © 2005 John Wiley & Sons, Ltd.