SIAM Journal on Numerical Analysis, Volume 60, Issue 3, Page 1331-1362, June 2022.
A framework to construct time-stable finite-difference schemes that apply boundary conditions strongly (or exactly) is presented for hyperbolic systems. A strong time-stability definition that applies to problems with homogeneous as well as nonhomogeneous boundary data is introduced. Sufficient conditions for strong time stability and conservation are derived for the linear advection equation and coupled system of hyperbolic equations using the energy method. Explicit boundary stencils and norms that satisfy those sufficient conditions are derived for various orders of accuracy. The discretization uses nonsquare derivative operators to allow stability and conservation conditions in terms of boundary data at grid points where physical boundary condition is directly injected and solution values at the rest of the grid points. Various linear and nonlinear numerical tests that verify the accuracy and stability of the derived stencils are presented.

中文翻译：

---

双曲系统有限差分格式中强边界条件的时间稳定性

SIAM 数值分析杂志，第 60 卷，第 3 期，第 1331-1362 页，2022 年 6 月。
为双曲系统提出了一个构建时间稳定的有限差分方案的框架，该方案强烈（或精确地）应用边界条件。引入了适用于齐次和非齐次边界数据问题的强时间稳定性定义。用能量法推导了线性平流方程和双曲方程耦合系统强时间稳定性和守恒的充分条件。满足这些充分条件的显式边界模板和规范是针对各种精度等级推导出来的。离散化使用非平方导数算子来允许在直接注入物理边界条件的网格点的边界数据和其余网格点的解值方面的稳定性和守恒条件。