2025/06/23 by Wasilij Barsukow, Barsukow, Wasilij, Mirco Ciallella +5 · 2 citations
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2506.21700
openalex publication_date 2025/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03
Classical Finite Volume methods for multi-dimensional problems include stabilization (e.g. via a Riemann solver), that is derived by considering several one-dimensional problems in different directions. Such methods therefore ignore a possibly existing balance of contributions coming from different directions, such as the one characterizing multi-dimensional stationary states. Instead of being preserved, they are usually diffused away by such methods. Stationarity preserving methods use a better suited stabilization term that vanishes at the stationary state, allowing the method to preserve it. This work presents a general approach to stationarity preserving Finite Volume methods for nonlinear conservation/balance laws. It is based on a multi-dimensional stationarity preserving quadrature strategy that allows to naturally introduce genuinely multi-dimensional numerical fluxes. The new methods are shown to significantly outperform existing ones even if the latter are of higher order of accuracy and even on non-stationary solutions.