A compact high-order gas-kinetic scheme (GKS) with spectral resolution will be presented and used in the simulation of acoustic and shock waves. Based on high-order gas evolution model, the GKS provides a time accurate solution at a cell interface, from which both time accurate flux function and flow variables can be obtained for updating cell averaged conservative flow variables and gradients. Based on cell-averaged flow variables and gradients, a reconstruction with compact stencil up to eighth-order spacial accuracy can be achieved, which include the nonlinear reconstruction for initial non-equilibrium state and linear reconstruction for the equilibrium one. The GKS unifies the nonlinear and linear reconstruction through a time evolution process at a cell interface from the non-equilibrium state to an equilibrium one. In the smooth acoustic wave region, the linear reconstruction will contribute mainly to the evolution. In the non-equilibrium shock region, the nonlinear reconstruction will play a dominant role.

中文翻译：

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具有类似光谱分辨率的声波和冲击波捕获紧凑的高阶气体动力学方案

将介绍一种具有光谱分辨率的紧凑高阶气体动力学方案 (GKS)，并将其用于声波和冲击波的模拟。基于高阶气体演化模型，GKS 提供了一个单元界面的时间精确解，从中可以获得时间精确的通量函数和流量变量，用于更新单元平均保守流量变量和梯度。基于单元平均流动变量和梯度，可以实现具有高达八阶空间精度的紧凑模板的重建，其中包括初始非平衡状态的非线性重建和平衡状态的线性重建。GKS 通过细胞界面从非平衡状态到平衡状态的时间演化过程统一了非线性和线性重建。在光滑的声波区域，线性重建将主要有助于演化。在非平衡冲击区域，非线性重建将起主导作用。