High-order gas kinetic flux solver for viscous compressible flow simulations

IF 1.7 4区工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

International Journal for Numerical Methods in Fluids Pub Date : 2024-02-08 DOI:10.1002/fld.5272

Lan Jiang, Jie Wu, Liming Yang, Hao Dong

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Abstract

Although the gas kinetic schemes (GKS) have emerged as one of the powerful tools for simulating compressible flows, they exhibit several shortcomings. Since the local solution of continuous Boltzmann equation with the Maxwellian distribution function is used to calculate the numerical fluxes at the cell interface, the flux expression in GKS is usually more complicated. In this paper, a high-order simplified gas kinetic flux solver (GKFS) is presented for simulating two-dimensional compressible flows. Circular function-based GKFS (C-GKFS), which simplifies the Maxwellian distribution function into the circular function, combined with an improved weighted essentially non-oscillatory (WENO-Z) scheme is applied to capture more details of the flow fields with fewer grids. As a result, a simple high-order accurate C-GKFS is obtained, which improves the computing efficiency and reduce its complexity to facilitate the practical application of engineering. A series of benchmark-test problems are simulated and good agreement can be obtained compared with the references, which demonstrate that the high-order C-GKFS can achieve the desired accuracy.

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用于粘性可压缩流模拟的高阶气体动通量求解器

尽管气体动力学方案（GKS）已成为模拟可压缩流动的强大工具之一，但它们也存在一些不足。由于连续波尔兹曼方程的局部解与麦克斯韦分布函数被用来计算单元界面上的数值通量，因此 GKS 中的通量表达式通常较为复杂。本文提出了一种用于模拟二维可压缩流的高阶简化气体动力学通量求解器（GKFS）。基于圆函数的 GKFS（C-GKFS）将麦克斯韦分布函数简化为圆函数，并结合改进的加权基本非振荡（WENO-Z）方案，以更少的网格捕捉流场的更多细节。因此，得到了一种简单的高阶精确 C-GKFS，提高了计算效率，降低了复杂度，便于工程实际应用。对一系列基准测试问题进行了仿真，结果与参考文献相比具有良好的一致性，证明高阶 C-GKFS 可以达到预期精度。

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

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.