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对流扩散方程的指数型摄动差分法 被引量:21

A PERTURBATIONAL FINITE DIFFERENCE SCHEME OFEXPONENTIAL TYPE FOR THE CONVECTION-DIFFUSION EQUATION
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摘要 改进了作者所提出的对流扩散方程四阶指数型摄动差分格式,并阐明其在高Reynolds数适应性和节省计算量方面的显著优点。指数型摄动差分法经改进后具有较为简便的形式,克服了其他紧致高阶格式不能使用于高Reynolds数问题的致命弱点。文中针对计算流体力学的基本困难,作一至三维流动模型方程和自然对流传热问题的精细计算,且以双精制算法检验格式的四阶精度,表明摄动差分法能在较粗的网格下给出相当准确的结果,十分显著地节省计算机时,并对“激波”和“边界层”等高Reynolds数效应有极高的分辨能力。 The perturbational fourth-order finite difference scheme of exponential type proposed by the authors is improved, by replacing the exponential coefficients in the source term perturbation with rational expressions, and is applied, aimed at the basic difficulties in computational fluid mechanics, to one-to three-dimensional model equations and a problem of natural convection with large Rayleigh-numbers, turning out the outstanding advantages of the perturbational scheme in such aspects as adaptability to flows with large Reynolds -numbers, resolution to 'shock wave'-and 'viscous boundary layer'-like effects, and saving computing CPU time.
出处 《计算物理》 CSCD 北大核心 1993年第2期197-207,共11页 Chinese Journal of Computational Physics
基金 国家攀登计划和自然科学基金
关键词 对流 扩散方程 摄动法 差分法 fluid mechanics, convection-diffusion equation, finite difference scheme, model equation, natural convection.
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