Quantifying residual numerical diffusion in flux-corrected transport algorithms
Quantifying residual numerical diffusion in flux-corrected transport algorithms
复制标题
量化通量校正传输算法中的残余数值扩散
DOI：
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发表时间：
1991
期刊：
影响因子：
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通讯作者：
F. Grinstein
中科院分区：
文献类型：
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作者：
D. Book;Chiping Li;G. Patnaik;F. Grinstein
流体动力学计算中的残余扩散是由基本线性算法中的有限阶近似引起的，包括有时由于数值原因而添加的平滑效果，以及在单调性保持算法（如通量校正传输（FCT））的情况下，通量限制器对陡峭剖面的非线性作用。一些广泛使用的FCT算法包含一个乘法常数，使反扩散系数降低0.01%-0.1%。用一个平滑变化的速度函数代替这个常数，当柯朗数为零时，这个函数等于1，这会导致线性扩散在流速为零时变为零。使用速度相关的反扩散系数，最大限度地减少数值拖尾的不连续性和相关的影响，在相邻的流。给出了计算实例。非零流速下的剩余扩散是非线性的，与问题有关。提出了一种在特定问题的背景下在任何给定代码中对其进行校准的方法，并将其应用于这里描述的FCT算法。
Residual diffusion in fluid-dynamics calculations results from the finite order of approximation in the underlying linear algorithm, including the effect of smoothing sometimes added for numerical reasons, and, in the case of monotonicity-preserving algorithms such as flux-corrected transport (FCT), the nonlinear action of the flux limiter on steep profiles. Some widely used FCT algorithms contain a multiplicative constant that reduces the antidiffusion coefficient by ∼0.01%–0.1%. Replacing this constant with a smoothly varying function of velocity which equals unity when the Courant number vanishes causes the linear diffusion to go to zero when the flow velocity does. The use of a velocity-dependent antidiffusion coefficient minimizes numerical smearing of discontinuities and associated effects in the neighboring flow. Computational examples are presented. The residual diffusion for nonzero flow speeds is nonlinear and problem dependent. A method is presented for calibrating it in any given code in the context of a particular problem, and is applied to the FCT algorithms described here.