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Nonlinear weighting process in ghost-cell immersed boundary methods for compressible flow
Journal of Computational Physics ( IF 4.1 ) Pub Date : 2021-02-17 , DOI: 10.1016/j.jcp.2021.110198
Hanahchim Choung , Vignesh Saravanan , Soogab Lee , Haeseong Cho

Computational challenges arise for the immersed boundary method (IBM) when dealing with compressible flow, where discontinuous and smoothly varying flow regions appear near the immersed boundary. The conventional ghost-cell IBM provides inaccurate results for smoothly varying regions when a low-order interpolation is used, or it suffers from a numerical instability for the discontinuous flow when a high-order interpolation is used. In this study, a new ghost-cell approach, nonlinear-weighted IBM (NWIBM), is developed to address the abovementioned issues. Inspired by a variety of weighted nonoscillatory interpolation methods, this work combines the high- and low-order polynomials during ghost-cell value estimation to enforce proper boundary conditions in the immersed boundary. A multidimensional smoothness indicator is designed to evaluate flow discontinuities. The nonlinear weighting obtained from the smoothness indicator makes the high-order polynomial dominant and the low-order polynomial negligible in the smoothly varying region, and vice versa in the discontinuous region. The enhanced performance and applicability of the proposed method were validated through various numerical tests in compressible flow. It was demonstrated that the NWIBM provides more stable and more accurate numerical solutions compared with conventional ghost-cell approaches.



中文翻译:

可压缩流的幻影单元浸入边界方法中的非线性加权过程

当处理可压缩流时,沉浸边界方法(IBM)会遇到计算挑战,其中在沉浸边界附近出现不连续且平滑变化的流动区域。当使用低阶插值时,常规的重影单元IBM不能为平滑变化的区域提供不准确的结果,或者当使用高阶插值时,其不连续流的数值不稳定。在这项研究中,开发了一种新的鬼单元方法,即非线性加权IBM(NWIBM),以解决上述问题。受到各种加权非振荡插值方法的启发,这项工作在重像元值估计期间结合了高阶和低阶多项式,以在沉浸边界中实施适当的边界条件。多维平滑度指示器旨在评估流量不连续性。从平滑度指示符获得的非线性加权使得在平滑变化的区域中高阶多项式占主导地位,而低阶多项式则可忽略,而在不连续区域中则相反。通过在可压缩流中进行各种数值测试,验证了所提方法的增强性能和适用性。事实证明,与传统的鬼像元方法相比,NWIBM提供了更稳定,更准确的数值解决方案。通过在可压缩流中进行各种数值测试,验证了所提方法的增强性能和适用性。事实证明,与传统的鬼像元方法相比,NWIBM提供了更稳定,更准确的数值解决方案。通过在可压缩流中进行各种数值测试,验证了所提方法的增强性能和适用性。事实证明,与传统的鬼像元方法相比,NWIBM提供了更稳定,更准确的数值解决方案。

更新日期:2021-02-22
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