@Article{CiCP-33-5,
author = {Yifei, Wan and Yinhua, Xia},
title = {A Hybrid WENO Scheme for Steady Euler Equations in Curved Geometries on Cartesian Grids},
journal = {Communications in Computational Physics},
year = {2023},
volume = {33},
number = {5},
pages = {1270--1331},
abstract = {<p style="text-align: justify;">For steady Euler equations in complex boundary domains, high-order shock-capturing schemes usually suffer not only from the difficulty of steady-state convergence but also from the problem of dealing with physical boundaries on Cartesian
grids to achieve uniform high-order accuracy. In this paper, we utilize a fifth-order
finite difference hybrid WENO scheme to simulate steady Euler equations, and the
same fifth-order WENO extrapolation methods are developed to handle the curved
boundary. The values of the ghost points outside the physical boundary can be obtained by applying WENO extrapolation near the boundary, involving normal derivatives acquired by the simplified inverse Lax-Wendroff procedure. Both equivalent expressions involving curvature and numerical differentiation are utilized to transform
the tangential derivatives along the curved solid wall boundary. This hybrid WENO
scheme is robust for steady-state convergence and maintains high-order accuracy in
the smooth region even with the solid wall boundary condition. Besides, the essentially non-oscillation property is achieved. The numerical spectral analysis also shows
that this hybrid WENO scheme has low dispersion and dissipation errors. Numerical
examples are presented to validate the high-order accuracy and robust performance of
the hybrid scheme for steady Euler equations in curved domains with Cartesian grids.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2022-0270},
url = {https://global-sci.com/article/79450/a-hybrid-weno-scheme-for-steady-euler-equations-in-curved-geometries-on-cartesian-grids}
}