2018/12/31 by José A. Carrillo, Serafim Kalliadasis, Sergio P. Perez +2 · 12 citations
Computer Science · Earth and Planetary Sciences · Engineering · Mathematics · Physics and Astronomy · #Applied mathematics #Aquatic and Environmental Studies #Computational Fluid Dynamics and Aerodynamics #Computer science #Dissipation #Dissipative system #Energy (signal processing) #Energy functional #Euler equations #Finite volume method #Gas Dynamics and Kinetic Theory #Mathematical analysis #Mathematics #Mechanics #Nonlinear system #Physics #Stability (learning theory) #Stationary state #Statistical physics #cond-mat.stat-mech #cs.NA #math.NA #physics.app-ph #physics.comp-ph #physics.flu-dyn
paper · pdf · doi:10.1137/18m1230050
published in Multiscale Modeling and Simulation 18(1), 502-541 (Society for Industrial and Applied Mathematics) · Videos from the simulations of this work are available at https://figshare.com/projects/Well-balanced_finite_volume_schemes_for_hydrodynamic_equations_with_general_free_energy/60122
openalex publication_date 2020/01/01 · arxiv created 2020/11/04 · arxiv updated 2020/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Well-balanced and free energy dissipative first- and second-order accurate finite-volume schemes are proposed for a general class of hydrodynamic systems with linear and nonlinear damping. The variation of the natural Lyapunov functional of the system, given by its free energy, allows for a characterization of the stationary states by its variation. An analogous property at the discrete level enables us to preserve stationary states at machine precision while keeping the dissipation of the discrete free energy. Performing a careful validation in a battery of relevant test cases, we show that these schemes can accurately analyze the stability properties of stationary states in challenging problems such as phase transitions in collective behavior, generalized Euler--Poisson systems in chemotaxis and astrophysics, and models in dynamic density functional theories.