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arXiv · 2506.03291

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

Wasilij Barsukow
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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.

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Wasilij Barsukow. 2025-06-03. An Active Flux method for the Euler equations based on the exact acoustic evolution operator. https://arxiv.org/abs/2506.03291

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