谱消去粘性谱元方法求解对流扩散方程  

Spectral vanishing viscosity method combined with spectral element method for convection-diffusion equation

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作  者:时永兴 

机构地区:[1]华电江苏能源有限公司句容发电厂,江苏镇江212400

出  处:《华电技术》2017年第10期25-29,共5页HUADIAN TECHNOLOGY

摘  要:针对谱元方法求解高雷诺数下对流扩散方程的稳定性问题,采用Chebyshev谱元方法结合谱消去粘性法求解一维对流扩散方程。利用特征分析法预测了数值方法的求解稳定性,通过数值算例验证了该解法的可行性,讨论了谱消去粘性参数对求解稳定性及数值精度的影响。结果表明:和谱元方法相比,谱消去粘性谱元方法求解对流扩散方程的稳定区域有了明显的扩大,在高雷诺数时能够获得具有较高精度的数值解;较大的谱消去粘性项有利于稳定区域的扩大,而在计算稳定的条件下较小的粘性项有利于数值精度的提高,所以适当地设置粘性项的大小,在保证计算稳定的同时提高数值精度。The Chebyshev spectral element method combined with spectral vanishing viscosity method is used to solve the onedimensional convection-diffusion equation,aiming at the instability phenomenon of spectral element method for convection-diffusion equation with high Reynolds number. The stability of the method is deduced with character analysis,and the feasibility of the proposed scheme is verified by a numerical example. The influence of spectral vanishing viscosity parameters on stability and accuracy is discussed. It is demonstrated that the stability and accuracy at high Reynolds number of spectral vanishing viscosity method are obviously improved compared with that of spectal element method. Larger spectal vanishing viscosity term is beneficial for extending the stable region and smaller viscosity term is beneficial for improving the accuracy at the condition of stable computation. The size of the viscosity term could be appropriately set to guarantee the stability and obtain numerical solution with high accuracy.

关 键 词:对流扩散方程 谱元法 谱消去粘性法 稳定性 高雷诺数 

分 类 号:O357.1[理学—流体力学]

 

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