A comparison of integration and interpolation Eulerian‐Lagrangian methods
A comparison of integration and interpolation Eulerian‐Lagrangian methods
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DOI：
10.1002/fld.1650210302
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发表时间：
1995-08
影响因子：
1.8
通讯作者：
A. Oliveira;A. Baptista
中科院分区：
文献类型：
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作者：
A. Oliveira;A. Baptista
在一维、常系数、保守问题的相对简单的背景下，系统地比较了几种求解输运方程的有限元欧拉-拉格朗日方法。采用形式分析和数值实验相结合的方法来表征特征线脚下浓度的不同处理所产生的稳定性和准确性。在所分析的方法中，那些以“整合”而不是“插值”的角度进行处理的方法往往具有更高的准确性。精确的集成导致无条件的稳定性和卓越的精度。正交积分只导致条件稳定性，但新导出的准则表明，稳定性限制相对温和，不应排除正交积分方法在一系列实际应用中的有用性。虽然结论不能直接扩展到多维和复杂的流动和几何形状，但结果应该为特定欧拉-拉格朗日输运模型的发展和行为提供有用的见解。
Selected finite element Eulerian-Lagrangian methods for the solution of the transport equation are compared systematically in the relatively simple context of 1D, constant coefficient, conservative problems. A combination of formal analysis and numerical experimentation is used to characterize the stability and accuracy that results from alternative treatments of the concentrations at the feet of the characteristic lines. Within the methods analyzed, those that approach such treatment with the perspective of ‘integration’ rather than ‘interpolation’ tend to have superior accuracy. Exact integration leads to unconditional stability and excellent accuracy. Quadrature integration leads only to conditional stability, but newly derived criteria show that stability restrictions are relatively mild and should not preclude the usefulness of quadrature integration methods in a range of practical applications. While conclusions cannot be extended directly to multiple dimensions and complex flows and geometries, results should provide useful insight to the development and behaviour of specific Eulerian-Lagrangian transport models.