We show that the classical fourth order accurate compact finite difference scheme with high order strong stability preserving time discretizations for convection diffusion problems satisfies a weak monotonicity property, which implies that a simple limiter can enforce the bound-preserving property without losing conservation and high order accuracy. Higher order accurate compact finite difference schemes satisfying the weak monotonicity will also be discussed.

翻译：本文证明了经典的四阶精度紧致有限差分格式结合高阶强稳定性保持时间离散方法在对流扩散问题中满足弱单调性性质。这一性质表明，通过简单的限制器可在不损失守恒性和高阶精度的前提下强制执行有界保持特性。此外，还将讨论满足弱单调性的高阶精度紧致有限差分格式。