Positivity-preserving numerical schemes for multidimensional advection
Positivity-preserving numerical schemes for multidimensional advection
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多维平流保正数值格式
DOI：
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发表时间：
1993
期刊：
影响因子：
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通讯作者：
A. Lock
中科院分区：
文献类型：
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作者：
B. P. Leonard;M. Macvean;A. Lock
本报告描述了基于统一三阶多项式插值算法 (UTOPIA) 的多维平流流显式、单时间步长、保守、有限体积方法的构建。特别关注流到网格角度相关的各向异性失真问题，这是按组件使用的一维方案的典型问题。三阶多维方案自动包含某些保证良好各向同性（和稳定性）的互差项。然而，以上一阶、基于多项式的平流方案不保留正性（单调性的多维模拟）。因此，寻求第一作者的通用通量限制器的多维概括。这是一个非常具有挑战性的问题。可以找到一个简单的通量限制器；但这会引入强烈的各向异性失真。一种更复杂的技术，限制部分通量，然后恢复各向同性保持交叉项，可以得到更令人满意的结果。测试用例仅限于二维；简要讨论了三维扩展。
This report describes the construction of an explicit, single time-step, conservative, finite-volume method for multidimensional advective flow, based on a uniformly third-order polynomial interpolation algorithm (UTOPIA). Particular attention is paid to the problem of flow-to-grid angle-dependent, anisotropic distortion typical of one-dimensional schemes used component-wise. The third-order multidimensional scheme automatically includes certain cross-difference terms that guarantee good isotropy (and stability). However, above first-order, polynomial-based advection schemes do not preserve positivity (the multidimensional analogue of monotonicity). For this reason, a multidimensional generalization of the first author's universal flux-limiter is sought. This is a very challenging problem. A simple flux-limiter can be found; but this introduces strong anisotropic distortion. A more sophisticated technique, limiting part of the flux and then restoring the isotropy-maintaining cross-terms afterwards, gives more satisfactory results. Test cases are confined to two dimensions; three-dimensional extensions are briefly discussed.