An Active Flux method for the Euler equations based on the exact acoustic evolution operator

TL;DR

This paper introduces a novel Active Flux numerical method for the Euler equations that employs an exact acoustic evolution operator and a third-order advection solver, improving accuracy and stability in multi-dimensional flow simulations.

Contribution

The paper presents a new Active Flux method combining exact acoustic evolution with a third-order advection operator, enhancing multi-dimensional Euler equation solutions.

Findings

Resolves multi-dimensional Riemann problems effectively

Handles low Mach number flows with stability

Achieves high-order accuracy in complex flow scenarios

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.