Simplification of the flux function for a high-order gas-kinetic evolution model
Simplification of the flux function for a high-order gas-kinetic evolution model
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DOI：
10.1016/j.jcp.2017.03.023
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发表时间：
2016-10
期刊：
影响因子：
--
通讯作者：
Guangzhao Zhou;Kun Xu;Feng Liu
中科院分区：
文献类型：
--
作者：
Guangzhao Zhou;Kun Xu;Feng Liu
求解Navier-Stokes方程的高阶（高于二阶）气体动力学格式近年来得到了研究。除了使用高阶重建技术外，在高阶气体动力学通量函数的平衡和非平衡气体分布函数的泰勒展开中还使用了许多术语。因此，在计算单元界面处气体分布函数的时间演化时，需要确定大量的系数。因此，高阶通量函数比二阶气体动力学格式的计算时间要长得多。本文旨在分两步简化演化模型。首先，重新定义与分布函数的二阶时空导数相关的系数，以减少计算成本；其次，在物理分析的基础上，可以在不损失准确性的情况下删除一些术语。结果表明，通过简化，高阶格式的计算效率得到了显著提高。此外，还设计了自适应数值黏度，使必要的数值耗散最小化。算例验证了该方法的准确性和鲁棒性。
High-order (higher-than 2nd-order) gas-kinetic schemes for solving the Navier–Stokes equations have been studied in recent years. In addition to the use of high-order reconstruction techniques, many terms are used in the Taylor expansion of the equilibrium and non-equilibrium gas distribution functions in the high-order gas kinetic flux function. Therefore, a large number of coefficients need to be determined in the calculation of the time evolution of the gas distribution function at cell interfaces. As a consequence, the high-order flux function takes much more computational time than that of a 2nd-order gas-kinetic scheme. This paper aims to simplify the evolution model by two steps. Firstly, the coefficients related to the 2nd-order spatial and temporal derivatives of a distribution function are redefined to reduce the computational cost. Secondly, based on the physical analysis, some terms can be removed without loss of accuracy. As a result, through the simplifications, the computational efficiency of the high-order scheme is increased significantly. In addition, a self-adaptive numerical viscosity is designed to minimize the necessary numerical dissipation. Several numerical examples are tested to demonstrate the accuracy and robustness of the current scheme.