A Shifted Boundary Method for the compressible Euler equations

• Published in: Journal of computational physics 2025-01, Vol.520, p.113512, Article 113512
• Main Authors: Zeng, Xianyi, Song, Ting, Scovazzi, Guglielmo
• Format: Article
• Language: English
• Subjects: Compressible flow; Euler equations; Explicit time integration; Finite element method; Shifted Boundary Method
• ISSN: 0021-9991
• DOI: 10.1016/j.jcp.2024.113512

The Shifted Boundary Method (SBM) is applied to compressible Euler flows, with and without shock discontinuities. The SBM belongs to the class of unfitted (or immersed, or embedded) finite element methods and avoids integration over cut cells (and the associated implementation/stability issues) by reformulating the original boundary value problem over a surrogate (approximate) computational domain. Accuracy is maintained by modifying the original boundary conditions using Taylor expansions. Hence the name of the method, that shifts the location and values of the boundary conditions. We specifically discuss the advantages the proposed method offers in avoiding spurious numerical artifacts in two scenarios: (a) when curved boundaries are represented by body-fitted polygonal approximations and (b) when the Kutta condition needs to be imposed in immersed simulations of airfoils. An extensive suite of numerical tests is included. •The Shifted Boundary Method (SBM) is applied to compressible Euler flows, with and without shocks.•The SBM avoids cut cells, by applying boundary conditions over an approximate boundary near the true boundary.•Boundary conditions on the approximate boundary use Taylor expansions that mimic the true boundary conditions.•The SBM delivers results equally accurate or more accurate than a body-fitted FEM.•The SBM allows for an improved imposition of the Kutta condition in airfoils.