Abstract In this paper we proposed the kinetic framework based fifth-order adaptive finite difference WENO schemes abbreviated as WENO-AO-K schemes to solve the compressible Euler equations, which are quasi-linear hyperbolic equations that can admit discontinuous solutions like shock and contact waves. The formulation of the proposed schemes is based on the kinetic theory where one can recover the Euler equations by applying a suitable moment method strategy to the Boltzmann equation. The kinetic flux vector splitting strategy is used in WENO-AO framework, which produces the computationally expensive error and exponential functions. Thus, to reduce the computational cost, a physically more relevant peculiar velocity based splitting strategy is used, which is more efficient than the kinetic flux vector splitting. High order of accuracy in time is achieved using the third-order total variation diminishing Runge–Kutta (TVD-RK) scheme. Several one- and two-dimensional test cases are solved for the compressible Euler equations using the proposed fifth-order WENO-AO-K schemes and the results are compared with conventional WENO-AO scheme. Proposed schemes capture the complex flow features in a smooth region accurately, and discontinuity is also well resolved. Error analysis of the proposed schemes shows optimal convergence rates in various norms.

中文翻译：

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基于动力学理论的可压缩欧拉方程多级自适应有限差分WENO格式

摘要 在本文中，我们提出了基于动力学框架的五阶自适应有限差分 WENO 方案（缩写为 WENO-AO-K 方案）来求解可压缩欧拉方程，这是一种准线性双曲方程，可以接纳冲击波和接触波等不连续解。 . 所提出方案的制定基于动力学理论，其中可以通过将合适的矩方法策略应用于 Boltzmann 方程来恢复 Euler 方程。在 WENO-AO 框架中使用了动力学通量矢量分裂策略，这会产生计算上昂贵的误差和指数函数。因此，为了降低计算成本，使用了一种物理上更相关的基于特殊速度的分裂策略，这比动力学通量矢量分裂更有效。使用三阶总变差减少 Runge-Kutta (TVD-RK) 方案可以实现高阶的时间精度。使用提出的五阶 WENO-AO-K 方案求解可压缩欧拉方程的几个一维和二维测试案例，并将结果与​​常规 WENO-AO 方案进行比较。所提出的方案准确地捕获了平滑区域中的复杂流特征，并且不连续性也得到了很好的解决。所提出方案的误差分析显示了各种规范下的最佳收敛速度。所提出的方案准确地捕获了平滑区域内的复杂流特征，并且不连续性也得到了很好的解决。所提出方案的误差分析显示了各种规范下的最佳收敛速度。所提出的方案准确地捕获了平滑区域中的复杂流特征，并且不连续性也得到了很好的解决。所提出方案的误差分析显示了各种规范下的最佳收敛速度。