This paper presents a new strategy to deal with the excessive diffusion that standard finite volume methods for compressible Euler equations display in the limit of low Mach number. The strategy can be understood as using centered discretizations for the acoustic part of the Euler equations and stabilizing them with a leap-frog-type ("sequential explicit") time integration, a fully explicit method. This time integration takes inspiration from time-explicit staggered grid numerical methods. In this way, advantages of staggered methods carry over to collocated methods. The paper provides a number of new collocated schemes for linear acoustic/Maxwell equations that are inspired by the Yee scheme. They are then extended to an all-speed method for the full Euler equations on Cartesian grids. By taking the opposite view and taking inspiration from collocated methods, the paper also suggests a new way of staggering the variables which increases the stability as compared to the traditional Yee scheme.

翻译：本文提出一种新策略，用于解决标准有限体积方法在低马赫数极限下处理可压缩欧拉方程时表现出的过度耗散问题。该策略可理解为对欧拉方程声学部分采用中心离散格式，并通过蛙跳型（"序贯显式"）时间积分——一种全显式方法——进行稳定化处理。该时间积分方法借鉴了时间显式交错网格数值方法的思想，从而将交错方法的优势延续至同位方法。受Yee格式启发，本文提出一系列适用于线性声学/麦克斯韦方程的新型同位格式，并将其推广至笛卡尔网格上全欧拉方程的全速域方法。通过逆向视角并借鉴同位方法，本文还提出一种新的变量交错方式，相较于传统Yee格式显著提升了稳定性。