A two-stage fourth-order gas-kinetic CPR method for the Navier-Stokes equations on triangular meshes
A two-stage fourth-order gas-kinetic CPR method for the Navier-Stokes equations on triangular meshes
复制标题
三角网格上纳维-斯托克斯方程的两级四阶气体动力学 CPR 方法
DOI：
10.1016/j.jcp.2021.110830
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发表时间：
2022
影响因子：
4.1
通讯作者：
Fu Song
中科院分区：
文献类型：
--
作者：
Zhang Chao;Li Qibing;Wang Z.J.;Li Jiequan;Fu Song
针对三角网格上的Navier-Stokes方程，提出了一种在空间和时间上都具有四阶精度的气体动力学格式。该方案结合了通过重建（CPR）框架的有效校正程序和鲁棒的气体动力学通量公式，该公式可以计算通量及其时间导数。通量及其时间导数的可用性使得采用有效的两阶段时间离散化来实现四阶时间精度变得简单。此外，通过气体动力学演化模型，将无粘通量和粘性通量进行了耦合和均匀计算，而没有对粘性通量进行单独处理。结果表明，该方法比传统的显式CPR方法更有效，该方法对粘性通量进行了单独处理，并采用了四阶龙格-库塔方法。此外，将一种鲁棒且精确的亚单元有限体积限制方法扩展到问题单元的CPR框架中，从而实现了流动不连续的亚单元分解。数值试验表明，该方法在亚音速到超音速范围内的无粘和粘性流动问题中具有较高的精度、效率和鲁棒性。
An efficient gas-kinetic scheme with fourth-order accuracy in both space and time is developed for the Navier-Stokes equations on triangular meshes. The scheme combines an efficient correction procedure via reconstruction (CPR) framework with a robust gas-kinetic flux formula, which computes both the flux and its time-derivative. The availability of the flux and its time-derivative makes it straightforward to adopt an efficient two-stage temporal discretization to achieve fourth-order time accuracy. In addition, through the gas-kinetic evolution model, the inviscid and viscous fluxes are coupled and computed uniformly without any separate treatment for the viscous fluxes. As a result, the current scheme is more efficient than traditional explicit CPR methods with a separate treatment for viscous fluxes, and a fourth-order Runge-Kutta approach. Furthermore, a robust and accurate subcell finite volume limiting procedure is extended to the CPR framework for troubled cells, resulting in subcell resolution of flow discontinuities. Numerical tests demonstrate the high accuracy, efficiency and robustness of the current scheme in a wide range of inviscid and viscous flow problems from subsonic to supersonic speeds.