We provide a framework for high-order discretizations of nonlinear scalar convection-diffusion equations that satisfy a discrete maximum principle. The resulting schemes can have arbitrarily high order accuracy in time and space, and can be stable and maximum-principle-preserving (MPP) with no step size restriction. The schemes are based on a two-tiered limiting strategy, starting with a high-order limiter-based method that may have small oscillations or maximum-principle violations, followed by an additional limiting step that removes these violations while preserving high order accuracy. The desirable properties of the resulting schemes are demonstrated through several numerical examples.

翻译：我们为非线性天线性对流-扩散方程式的高度分解提供了框架,这些方程式满足了离散的最大原则,由此形成的计划在时间和空间上可能任意地具有高度的顺序精确性,并且能够保持稳定和最大的原则保全(MPP),没有步骤大小限制,这些计划基于一种两级限制战略,首先采用基于高阶的限量法,该方法可能具有小的振荡或最高原则违反,随后又采取了额外的限制性步骤,消除这些违规行为,同时保持高度的顺序精确性,由此形成的计划的适当性质通过几个数字例子得到证明。