AI 中文总结
研究为双曲守恒律系统开发新自适应数值格式，利用平滑度指标分区，在平滑区域采用新拟线性七阶和九阶格式，经气体动力学欧拉方程实验验证，新格式数值耗散少、分辨率更高。
AI 中文摘要
我们为一维和二维双曲守恒律系统开发了新的自适应数值格式。该方法依赖于使用平滑度指标自动将计算域划分为平滑和非平滑（“粗糙”）区域。然后我们遵循最近在[S. Chu, P. Feng, V. A. Kolotilov, A. Kurganov, and V. V. Ostapenko, Commun. Comput. Phys., accepted]中引入的格式自适应策略，但在平滑区域中，我们使用新的拟线性七阶和九阶格式，而不是那里使用的拟线性（QL）五阶有限差分格式。一系列气体动力学欧拉方程的数值实验表明，与在平滑区域使用QL五阶格式的对应格式相比，新的自适应格式具有更少的数值耗散并实现了更高的分辨率。
英文摘要
We develop new adaptive numerical schemes for one- and two-dimensional hyperbolic systems of conservation laws. The methodology relies on the use of a smoothness indicator to automatically partition the computational domain into smooth and nonsmooth (``rough``) regions. We then follow the scheme adaption strategy recently introduced in [S. Chu, P. Feng, V. A. Kolotilov, A. Kurganov, and V. V. Ostapenko, Commun. Comput. Phys., accepted], but instead of the quasi-linear (QL) fifth-order finite-difference scheme used there, we employ the new QL seventh- and ninth-order schemes in the smooth regions. A series of numerical experiments for the Euler equations of gas dynamics demonstrates that the new adaptive schemes contain a smaller amount of numerical dissipation and achieve higher resolution compared with their counterpart that uses the QL fifth-order scheme in the smooth areas.
