A third-order gas-kinetic CPR method for the Euler and Navier–Stokes equations on triangular meshes
A third-order gas-kinetic CPR method for the Euler and Navier–Stokes equations on triangular meshes
复制标题
三角形网格上欧拉和纳维斯托克斯方程的三阶气体动力学 CPR 方法
DOI：
10.1016/j.jcp.2018.02.040
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发表时间：
2018
影响因子：
4.1
通讯作者：
Wang Z.J.
中科院分区：
文献类型：
--
作者：
Zhang Chao;Li Qibing;Fu Song;Wang Z.J.
针对三角网格上的欧拉和纳维-斯托克斯方程，开发了基于重构修正程序 (CPR) 框架的三阶精确气体动力学方案。该方案将 CPR 公式的准确性和效率与气体运动通量求解器的多维特性和鲁棒性相结合。与高阶有限体积气体动力学方法相比，当前方案通过避免非结构化网格上的宽模板而更加紧凑和高效。与传统的CPR方法对无粘性和粘性项进行不同处理不同，当前方案中的无粘性和粘性通量通过动力学演化模型统一耦合和计算。此外，本方案采用完全耦合的空间和时间气体分布函数进行通量评估，在单个步骤内实现了空间和时间上的高阶精度。对各种流动问题的数值测试，从几乎不可压缩的流动到具有强冲击的超音速流动，对于无粘性和粘性问题，都证明了本方案的高精度和高效性。
A third-order accurate gas-kinetic scheme based on the correction procedure via reconstruction (CPR) framework is developed for the Euler and Navier–Stokes equations on triangular meshes. The scheme combines the accuracy and efficiency of the CPR formulation with the multidimensional characteristics and robustness of the gas-kinetic flux solver. Comparing with high-order finite volume gas-kinetic methods, the current scheme is more compact and efficient by avoiding wide stencils on unstructured meshes. Unlike the traditional CPR method where the inviscid and viscous terms are treated differently, the inviscid and viscous fluxes in the current scheme are coupled and computed uniformly through the kinetic evolution model. In addition, the present scheme adopts a fully coupled spatial and temporal gas distribution function for the flux evaluation, achieving high-order accuracy in both space and time within a single step. Numerical tests with a wide range of flow problems, from nearly incompressible to supersonic flows with strong shocks, for both inviscid and viscous problems, demonstrate the high accuracy and efficiency of the present scheme.