Fernández-Fidalgo, JavierNogueira, XesúsRamírez, LuisColominas, IgnasiClain, StéphaneGrupos de investigación-Grupo de Métodos Numéricos na Enxeñería2024-01-292024-01-292020Fernández-Fidalgo, J., Clain, S., Ramírez, L., Colominas, I., & Nogueira, X. (2020). Very high-order method on immersed curved domains for finite difference schemes with regular Cartesian grids. Computer Methods in Applied Mechanics and Engineering, 360, 112782. https://doi.org/10.1016/j.cma.2019.112782http://hdl.handle.net/2183/35190Versión aceptada de https://doi.org/10.1016/j.cma.2019.112782[Abstract:] A new very high-order technique for solving conservation laws with curved boundary domains is proposed. A Finite Difference scheme on Cartesian grids is coupled with an original ghost cell method that provide accurate approximations for smooth solutions. The technology is based on a specific least square method with restrictions that enables to handle general Robin conditions. Several examples in two-dimensional geometries are presented for the unsteady Convection–Diffusion equation and the Euler equations. A fifth-order WENO scheme is employed with matching fifth-order reconstruction at the boundaries. Arbitrary high-order reconstruction for smooth flows is achievable independently of the underlying differential equation since the method works as a black-box dedicated to boundary condition treatment.engAttribution-NonCommercial-NoDerivs 4.0 International (CC BY-NC-ND)https://creativecommons.org/licenses/by-nc-nd/4.0/High-order schemesCompressible flowsCartesian gridsFinite differenceEmbedded boundaryRODjournal articleopen access10.1016/j.cma.2019.112782