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首页> 外文期刊>Journal of Scientific Computing >On the Linear Stability of the Fifth-Order WENO Discretization
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On the Linear Stability of the Fifth-Order WENO Discretization

机译：五阶WENO离散化的线性稳定性

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摘要

We study the linear stability of the fifth-order Weighted Essentially Non-Oscillatory spatial discretization (WEN05) combined with explicit time stepping applied to the one-dimensional advection equation. We show that it is not necessary for the stability domain of the time integrator to include a part of the imaginary axis. In particular, we show that the combination of WEN05 with either the forward Euler method or a two-stage, second-order Runge-Kutta method is linearly stable provided very small time step-sizes are taken. We also consider fifth-order multistep time discretizations whose stability domains do not include the imaginary axis. These are found to be linearly stable with moderate time steps when combined with WENO5. In particular, the fifth-order extrapolated BDF scheme gave superior results in practice to high-order Runge-Kutta methods whose stability domain includes the imaginary axis. Numerical tests are presented which confirm the analysis.
机译：我们研究了一阶对流方程的五阶加权基本非振荡空间离散化（WEN05）与显式时间步长的线性稳定性。我们表明，时间积分器的稳定性域不必包括虚轴的一部分。特别是，我们表明，如果采用非常小的时间步长，则将WEN05与正向Euler方法或两阶段，二阶Runge-Kutta方法的组合线性稳定。我们还考虑了其​​稳定性域不包括虚轴的五阶多步时间离散化。当与WENO5结合使用时，它们具有中等的时间步长，具有线性稳定性。尤其是，五阶外推BDF方案在实践中优于其稳定性域包括虚轴的高阶Runge-Kutta方法。数值测试证实了分析结果。

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