2024/09/17 by Yang Li, Xu Wu, Li, Yang +8 · 2 citations
Engineering · Mathematics · #65M20(Primary) #76D05(Primary) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2409.11255
openalex publication_date 2024/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Inspired by the unconstrained PPE (UPPE) formulation [Liu, Liu, & Pego 2007 Comm. Pure Appl. Math., 60 pp. 1443], we previously proposed the GePUP formulation [Zhang 2016 J. Sci. Comput., 67 pp. 1134] for numerically solving the incompressible Navier-Stokes equations (INSE) on no-slip domains. In this paper, we propose GePUP-E and GePUP-ES, variants of GePUP that feature (a) electric boundary conditions with no explicit enforcement of the no-penetration condition, (b) equivalence to the no-slip INSE, (c) exponential decay of the divergence of an initially non-solenoidal velocity, and (d) monotonic decrease of the kinetic energy. Different from UPPE, the GePUP-E and GePUP-ES formulations are of strong forms and are designed for finite volume/difference methods under the framework of method of lines. Furthermore, we develop semi-discrete algorithms that preserve (c) and (d) and fully discrete algorithms that are fourth-order accurate for velocity both in time and in space. These algorithms employ algebraically stable time integrators in a black-box manner and only consist of solving a sequence of linear equations in each time step. Results of numerical tests confirm our analysis.