An Active Flux method for the Euler equations based on the exact acoustic evolution operator
Abstract
A new Active Flux method for the multi-dimensional Euler equations is based on an additive operator splitting into acoustics and advection. The acoustic operator is solved in a locally linearized manner by using the exact evolution operator. The nonlinear advection operator is solved at third order accuracy using a new approximate evolution operator. To simplify the splitting, the new method uses primitive variables for the point values and for the reconstruction. In order to handle discontinuous solutions, a blended bound preserving limiting is used, that combines a priori and a posteriori approaches. The resulting method is able to resolve multi-dimensional Riemann problems as well as low Mach number flow, and has a large domain of stability.
Cite
@article{arxiv.2506.03291,
title = {An Active Flux method for the Euler equations based on the exact acoustic evolution operator},
author = {Wasilij Barsukow},
journal= {arXiv preprint arXiv:2506.03291},
year = {2025}
}