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.

中文翻译：

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用于粘性可压缩流模拟的高阶气体动力学通量求解器

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，但它们也存在一些缺点。由于采用麦克斯韦分布函数的连续玻尔兹曼方程的局部解来计算细胞界面处的数值通量，因此GKS中的通量表达式通常比较复杂。在本文中，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）。基于循环函数的 GKFS (C-GKFS) 将麦克斯韦分布函数简化为循环函数，并结合改进的加权本质非振荡 (WENO-Z) 方案，以更少的网格捕获流场的更多细节。从而得到简单的高阶精确C-GKFS，提高了计算效率，降低了复杂度，便于工程实际应用。模拟了一系列基准测试问题，与参考文献相比，得到了很好的一致性，这表明高阶C-GKFS能够达到预期的精度。