一种用于可压缩欧拉和纳维-斯托克斯方程的紧凑型第三阶气体动力学格式
A Compact Third-order Gas-kinetic Scheme for Compressible Euler and Navier-Stokes Equations
AI总结：
本文提出了一种用于可压缩欧拉和纳维-斯托克斯方程的紧凑型第三阶气体动力学格式，该方法通过高阶气体演化模型实现高阶精度，无需使用高斯点和多阶段龙格-库塔时间步进技术，具有良好的激波捕捉能力。
摘要：
在本文中，提出了一种用于可压缩欧拉和纳维-斯托克斯方程的紧凑型第三阶气体动力学格式。开发此类高阶格式的可行性源于使用高阶气体演化模型。除了评估时间依赖的通量函数跨单元界面外，高阶气体演化模型还提供了单元界面处时间依赖的流变量精确解。因此，当前方案不仅更新每个控制体积内的单元平均守恒流变量，还追踪单元界面处的流变量在下一个时间层。结果，利用单元平均值和单元界面值，当前方案可以实现紧凑的高阶重建。与使用弱形式在间断伽辽金（DG）方法中实现高阶精度不同，当前方案基于强解，其中从分段不连续的高阶初始数据开始的流演化被精确跟踪。单元界面的时间依赖流变量可用于下一个时间步的初始数据重建。即使具有紧凑的 stencil，当前方案在光滑流区域具有第三阶精度，并在不连续区域具有良好的激波捕捉特性。许多测试案例用于验证当前方案。与许多其他高阶方案相比，当前方法避免了沿单元界面评估通量时使用高斯点和多阶段龙格-库塔时间步进技术。
英文摘要：
In this paper, a compact third-order gas-kinetic scheme is proposed for the compressible Euler and Navier-Stokes equations. The main reason for the feasibility to develop such a high-order scheme with compact stencil, which involves only neighboring cells, is due to the use of a high-order gas evolution model. Besides the evaluation of the time-dependent flux function across a cell interface, the high-order gas evolution model also provides an accurate time-dependent solution of the flow variables at a cell interface. Therefore, the current scheme not only updates the cell averaged conservative flow variables inside each control volume, but also tracks the flow variables at the cell interface at the next time level. As a result, with both cell averaged and cell interface values the high-order reconstruction in the current scheme can be done compactly. Different from using a weak formulation for high-order accuracy in the Discontinuous Galerkin (DG) method, the current scheme is based on the strong solution, where the flow evolution starting from a piecewise discontinuous high-order initial data is precisely followed. The cell interface time-dependent flow variables can be used for the initial data reconstruction at the beginning of next time step. Even with compact stencil, the current scheme has third-order accuracy in the smooth flow regions, and has favorable shock capturing property in the discontinuous regions. Many test cases are used to validate the current scheme. In comparison with many other high-order schemes, the current method avoids the use of Gaussian points for the flux evaluation along the cell interface and the multi-stage Runge-Kutta time stepping technique.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
