All-Speed Numerical Methods for the Euler Equations via a Sequential Explicit Time Integration

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