论文标题
基于新的局部平滑度指示器的自适应高阶A-Weno方案
Adaptive High-Order A-WENO Schemes Based on a New Local Smoothness Indicator
论文作者
论文摘要
我们为保护法的双曲线系统开发了新的自适应替代加权基本非振荡（A-WENO）方案。这些新方案采用了最近提出的基于局部特征分解的基于中央风的数值通量，三阶段的三阶强稳定性保留runge-kutta time Intemitator和第五阶Weno-Z插值。自适应策略是通过仅在借助平滑度指示器的帮助下应用有限的插值来实现的，在计算域的各个部分中，将解决方案识别为``粗糙''。我们开发和使用新的简单且健壮的局部平滑度指示器（LSI），该指标（LSI）应用于在ODE求解器的三个阶段中计算出的解决方案。 在气体动力学的Euler方程上测试了新的LSI和自适应A-WENO方案。我们使用压力实施了拟议的LSI，该压力在接触不连续性下保持平稳，而我们的目标是检测其他``粗糙''区域，并主要在冲击波附近应用有限的插值。我们证明了新的自适应方案是高度准确，非振荡和强大的。他们的表现胜过完全有限的对应物（具有相同数值通量和ode求解器的A-Weno方案，但在任何地方都使用了Weno-Z插值），而计算上的昂贵也不那么昂贵。
We develop new adaptive alternative weighted essentially non-oscillatory (A-WENO) schemes for hyperbolic systems of conservation laws. The new schemes employ the recently proposed local characteristic decomposition based central-upwind numerical fluxes, the three-stage third-order strong stability preserving Runge-Kutta time integrator, and the fifth-order WENO-Z interpolation. The adaptive strategy is implemented by applying the limited interpolation only in the parts of the computational domain where the solution is identified as ``rough'' with the help of a smoothness indicator. We develop and use a new simple and robust local smoothness indicator (LSI), which is applied to the solutions computed at each of the three stages of the ODE solver. The new LSI and adaptive A-WENO schemes are tested on the Euler equations of gas dynamics. We implement the proposed LSI using the pressure, which remains smooth at contact discontinuities, while our goal is to detect other ``rough'' areas and apply the limited interpolation mostly in the neighborhoods of the shock waves. We demonstrate that the new adaptive schemes are highly accurate, non-oscillatory, and robust. They outperform their fully limited counterparts (the A-WENO schemes with the same numerical fluxes and ODE solver but with the WENO-Z interpolation employed everywhere) while being less computationally expensive.
