Enhanced freestream-preserving finite difference method based on MUSCL for numerical computation of laminar flow

IF 2.8 3区工程技术 Q2 MECHANICS

Theoretical and Computational Fluid Dynamics Pub Date : 2025-06-13 DOI:10.1007/s00162-025-00745-1

Tianen Guan, Zijia Huang, Chunguang Xu

引用次数: 0

Abstract

The implementation of the finite-difference method in curvilinear coordinates necessitates coordinate transformations, where violations of the Geometric Conservation Law (GCL) lead to loss of freestream preservation. This failure mechanism typically manifests as numerical instability or spurious physical artifacts in simulations. In this paper, we developed a freestream-preserving Monotone Upstream-centered Scheme for Conservation Laws (MUSCL) to solve viscous problems on perturbed grids. The geometrically induced errors are eliminated with the satisfaction of GCL. The central difference method is used for the computation of viscous flux terms, and the least squares method is introduced to enhance the accuracy and robustness of this scheme for solving subsonic viscous problems. The results of several viscous numerical tests demonstrate the reliable freestream-preserving property of the new method compared to MUSCL.

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层流数值计算中基于MUSCL的增强保持自由流有限差分法

在曲线坐标中实现有限差分法需要进行坐标变换，违反几何守恒定律（GCL）将导致自由流保存的丧失。这种失效机制通常表现为数值不稳定或模拟中的虚假物理伪像。本文提出了一种保持自由流的单调上游中心守恒律格式（MUSCL）来解决扰动网格上的粘性问题。在满足GCL要求的情况下，消除了几何误差。采用中心差分法计算粘性通量项，并引入最小二乘法提高该格式在求解亚音速粘性问题时的精度和鲁棒性。若干粘性数值试验结果表明，与MUSCL相比，新方法具有可靠的自由流保持性能。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Theoretical and Computational Fluid Dynamics 物理-力学

CiteScore

5.80

自引率

2.90%

发文量

审稿时长

>12 weeks

期刊介绍： Theoretical and Computational Fluid Dynamics provides a forum for the cross fertilization of ideas, tools and techniques across all disciplines in which fluid flow plays a role. The focus is on aspects of fluid dynamics where theory and computation are used to provide insights and data upon which solid physical understanding is revealed. We seek research papers, invited review articles, brief communications, letters and comments addressing flow phenomena of relevance to aeronautical, geophysical, environmental, material, mechanical and life sciences. Papers of a purely algorithmic, experimental or engineering application nature, and papers without significant new physical insights, are outside the scope of this journal. For computational work, authors are responsible for ensuring that any artifacts of discretization and/or implementation are sufficiently controlled such that the numerical results unambiguously support the conclusions drawn. Where appropriate, and to the extent possible, such papers should either include or reference supporting documentation in the form of verification and validation studies.