In this paper, we construct the monotonicity-preserving Lax–Wendroff (MP-Lax–Wendroff) scheme based on the MP scheme as proposed by Suresh and Huynh [11], which is a high-order and high-resolution method for hyperbolic conservation laws. It is well known that the total-variation-diminishing (TVD) methods possess the order reduction at smooth extremum points. However, the MP scheme not only preserves the non-oscillatory behavior of the procedure, but also prevents the order reduction of the method. We provide an analysis of the MP procedure using the numerical Lax–Wendroff flux sophistically in detail. Due to lack of robustness of the MP scheme, a rigorous and efficient MP-Lax–Wendroff scheme is introduced to enhance the robustness of the MP process. This means that a TVD numerical flux is applied to damp the oscillations at disturbed discontinuity points to get the high-resolution property. Therefore, we apply this idea to construct the improved MP-Lax–Wendroff scheme (we call it MP-R-Lax–Wendroff scheme). The computational performance of the MP-R-Lax–Wendroff scheme for linear and nonlinear hyperbolic conservation laws is conducted through some prototype examples which in turn validate our theoretical results.

在本文中，我们基于Suresh和Huynh [11]提出的MP方案，构造了保持单调性的Lax-Wendroff（MP-Lax-Wendroff）方案，这是一种高阶，高分辨率的双曲式保存方法法律。众所周知，总变化量减少（TVD）方法在平滑极值点处具有阶数减少。但是，MP方案不仅保留了程序的非振荡行为，而且还防止了方法的降阶。我们详细地使用数值Lax–Wendroff通量提供了MP程序的分析。由于MP方案缺乏鲁棒性，因此引入了严格而有效的MP-Lax-Wendroff方案来增强MP过程的鲁棒性。这意味着应用TVD数值通量来衰减受干扰的不连续点处的振荡，从而获得高分辨率特性。因此，我们将这个想法应用于构建改进的MP-Lax-Wendroff方案（我们将其称为MP-R-Lax-Wendroff方案）。通过一些原型示例，对线性和非线性双曲守恒律进行了MP-R-Lax–Wendroff方案的计算性能，这反过来验证了我们的理论结果。