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Solution-based adaptive mesh redistribution applied to harmonic balance solvers

机译：基于解决方案的自适应网格重新分配应用于谐波平衡求解器

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摘要

A primary source of inaccuracy in numerical simulations is due to errors that are introduced into the solution via the discretization of the continuous governing equations over the computational domain. By increasing the grid resolution in regions with high flow gradients and large curvatures using a solution-adaptive approach, these discretization errors can be reduced. In this paper, an adaptive mesh technique is presented that can efficiently cluster the grid nodes in sensitive regions by redistribution and relocation of the grid nodes. This adaptive technique is specifically important to unsteady periodic flow cases where the length scales of the flow features (such as shocks, boundary layer, and separation zones) can differ between time instances. The proposed technique is developed - for the first time in the literature - for a harmonic balance method to efficiently model unsteady periodic flows. To study the performance of the proposed technique in improving the accuracy of the flow solver, steady and unsteady flow cases are studied. Numerical results show that the adaptive mesh redistribution technique is capable of efficiently increasing the accuracy of the numerical solver with a relatively low computational overhead. (C) 2018 Elsevier Masson SAS. All rights reserved.
机译：数值模拟中不准确的主要根源是由于在计算域上通过连续控制方程的离散化而引入到解决方案中的误差。通过使用解决方案自适应方法在具有高流量梯度和大曲率的区域中提高网格分辨率，可以减少这些离散误差。在本文中，提出了一种自适应网格技术，该技术可以通过重新分配和重新布置网格节点来有效地对敏感区域中的网格节点进行聚类。对于不稳定的周期性流动情况，这种自适应技术特别重要，在这种情况下，流动特征（如冲击波，边界层和分离带）的长度尺度在时间点之间可能会有所不同。所提出的技术是文献中的第一次，它是一种谐波平衡方法，可以有效地对非稳态周期性流动进行建模。为了研究所提出技术在提高流量求解器精度方面的性能，研究了稳态和非稳态流动情况。数值结果表明，自适应网格重新分配技术能够以相对较低的计算开销有效地提高数值求解器的精度。 （C）2018 Elsevier Masson SAS。版权所有。

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