2022/03/28 by Rémi Bourgeois, Pascal Tremblin, Bourgeois, Rémi +5 · 1 citation
Earth and Planetary Sciences · Engineering · Physics and Astronomy · #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Meteorological Phenomena and Simulations #Model Reduction and Neural Networks #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2203.14596
openalex publication_date 2022/03/28 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28
In this paper, we propose a modification of an acoustic-transport operator splitting Lagrange-projection method for simulating compressible flows with gravity. The original method involves two steps that respectively account for acoustic and transport effects. Our work proposes a simple modification of the transport step, and the resulting modified scheme turns out to be a flux-splitting method. This new numerical method is less computationally expensive, more memory efficient, and easier to implement than the original one. We prove stability properties for this new scheme by showing that under classical CFL conditions, the method is positivity preserving for mass, energy and entropy satisfying. The flexible flux-splitting structure of the method enables straightforward extensions of the method to multi-dimensional problems (with respect to space) and high-order discretizations that are presented in this work. We also propose an interpretation of the flux-splitting solver as a relaxation approximation. Both the stability and the accuracy of the new method are tested against one-dimensional and two-dimensional numerical experiments that involve highly compressible flows and low-Mach regimes.