We develop a simple, high-order, conservative and robust positivity-preserving sweeping procedure for the density and the nonlinear pressure function in the compressible Euler equations. Using the scaling limiter in Zhang and Shu (2010), we obtain a nontrivial extension of the scalar sweeping technique in Liu, Cheng, and Shu (2016) for the positivity of pressure. The sweeping procedure developed in this paper is a post-processing technique, which can be applied to any concave functions of the conserved variables in hyperbolic conservation law systems. Thus, it has applications beyond the Euler equations. This procedure preserves positivity and conservation of physical quantities without destroying the accuracy of the underlying scheme. The algorithm works for general schemes including finite difference, finite-volume and discontinuous Galerkin methods; however, in this paper we focus on finite-difference weighted essentially non-oscillatory (WENO) methods. We provide numerical tests of the fifth order finite difference WENO scheme to demonstrate the accuracy and robustness of the technique.

翻译：本文针对可压缩欧拉方程中的密度和非线性压力函数，提出了一种简洁、高阶、守恒且鲁棒的保正性扫描方法。基于Zhang和Shu（2010）提出的缩放限制器，我们将Liu、Cheng和Shu（2016）中用于压力保正性的标量扫描技术进行了非平凡扩展。本文发展的扫描方法是一种后处理技术，可应用于双曲守恒律系统中守恒变量的任意凹函数，因此其应用范围超越欧拉方程。该过程在保持物理量守恒性与正性的同时，不会破坏底层格式的精度。该算法适用于有限差分、有限体积及间断伽辽金等通用格式，但本文重点研究有限差分加权本质无振荡（WENO）方法。我们通过五阶有限差分WENO格式的数值算例，验证了该技术的精度与鲁棒性。