Linear Discontinuity Sharpening for Highly Resolved and Robust Magnetohydrodynamics Simulations

IF 1.8 4区 工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Tomohiro Mamashita, Gaku Fukushima, Keiichi Kitamura
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引用次数: 0

Abstract

This study applies a reconstruction scheme, “hybrid MUSCL–THINC” for finite volume methods developed by Chiu et al., to magnetohydrodynamics (MHD) simulations. The scheme is a hybrid of monotone upstream-centered schemes for conservation law (MUSCL) and a tangent of hyperbola interface capturing (THINC) scheme. THINC sharply captures discontinuous distributions of physical quantities by using a hyperbolic tangent function. Our investigation reveals that hybrid MUSCL–THINC is more oscillatory in MHD simulations than in gas dynamics simulations, owing to the greater number of physical variables and associated complex waves in MHD. Analytical results demonstrate that artificial compression by THINC is excessive for MHD shock waves, whereas it is effective for linear discontinuities, such as contact discontinuities. Therefore, we propose a modification in which the artificial compression by THINC is weakened in the vicinity of nonlinear discontinuities and applied only to linear regions. The new scheme is tested using one- and two-dimensional MHD problems, and the results demonstrate that the scheme sharply captures linear discontinuities while avoiding numerical oscillations due to excessive artificial compression.

Abstract Image

用于高分辨率和鲁棒磁流体动力学模拟的线性不连续锐化
本研究将Chiu等人开发的用于有限体积方法的“hybrid MUSCL-THINC”重建方案应用于磁流体动力学(MHD)模拟。该方案是一种以上游为中心的单调守恒律方案(MUSCL)和双曲线切线界面捕获方案(THINC)的混合方案。THINC通过使用双曲正切函数来捕捉物理量的不连续分布。我们的研究表明,由于MHD中更多的物理变量和相关的复杂波,混合MUSCL-THINC在MHD模拟中比在气体动力学模拟中更具振荡性。分析结果表明,对于MHD冲击波,THINC的人工压缩是过度的,而对于线性不连续面,如接触不连续面,THINC是有效的。因此,我们提出了一种改进方法,即在非线性不连续区域附近减弱THINC的人工压缩,并仅应用于线性区域。利用一维和二维MHD问题对新方案进行了测试,结果表明,该方案可以很好地捕捉线性不连续,同时避免了由于过度人为压缩引起的数值振荡。
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来源期刊
International Journal for Numerical Methods in Fluids
International Journal for Numerical Methods in Fluids 物理-计算机:跨学科应用
CiteScore
3.70
自引率
5.60%
发文量
111
审稿时长
8 months
期刊介绍: The International Journal for Numerical Methods in Fluids publishes refereed papers describing significant developments in computational methods that are applicable to scientific and engineering problems in fluid mechanics, fluid dynamics, micro and bio fluidics, and fluid-structure interaction. Numerical methods for solving ancillary equations, such as transport and advection and diffusion, are also relevant. The Editors encourage contributions in the areas of multi-physics, multi-disciplinary and multi-scale problems involving fluid subsystems, verification and validation, uncertainty quantification, and model reduction. Numerical examples that illustrate the described methods or their accuracy are in general expected. Discussions of papers already in print are also considered. However, papers dealing strictly with applications of existing methods or dealing with areas of research that are not deemed to be cutting edge by the Editors will not be considered for review. The journal publishes full-length papers, which should normally be less than 25 journal pages in length. Two-part papers are discouraged unless considered necessary by the Editors.
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