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| Comparison of the Fourier-Legendre spectral element method and the finite difference method on the numerical diffusion in polar coordinate |
| Received:February 23, 2012 Revised:July 29, 2012 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx201303015 |
| KeyWord:spectral element method finite difference method upwind difference scheme Navier-Stokes equations Legendre polynomials Fourier polynomials |
| Author | Institution |
| 梅欢 |
重庆大学资源及环境科学学院 工程力学系, 重庆 |
| 曾忠 |
重庆大学资源及环境科学学院 工程力学系, 重庆 ;煤矿灾害动力学与控制国家重点实验室重庆大学, 重庆 |
| 邱周华 |
重庆大学资源及环境科学学院 工程力学系, 重庆 |
| 李亮 |
重庆大学资源及环境科学学院 工程力学系, 重庆 |
| 姚丽萍 |
重庆大学资源及环境科学学院 工程力学系, 重庆 |
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| Abstract: |
| For solving the Navier-Stokes equations in polar coordinates,a Fourier-Legendre spectral element method (SEM) with Gauss-Radau quadrature points in the radical direction for the element involving the origin r=0 is proposed to avoid the coordinate singularity 1/r.The time-splitting method is employed in the temporal discretization.A numerical isotope model is applied to track the isotope transport and therefore to evaluate the accuracy of numerical simulation.The isotope equation is solved by both the SEM and a finite-difference method (FDM) with an upwind difference scheme in the flows driven by a steady and an accelerated crucible rotations.The results demonstrate that a severe false numerical diffusion appears in FDM with the first-order upwind difference scheme.The accuracy of the second-order upwind scheme is higher than that of the first-order upwind scheme,and a dense mesh is helpful to alleviate the false diffusion effectively.However,the SEM exhibits an obvious advantage to achieve the high accuracy solution with even relative fewer nodes. |