Year: 2023
Author: Yifei Wan, Yinhua Xia
Communications in Computational Physics, Vol. 33 (2023), Iss. 5 : pp. 1270–1331
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2022-0270
Communications in Computational Physics, Vol. 33 (2023), Iss. 5 : pp. 1270–1331
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 62
Keywords: Euler equations steady-state convergence curved boundary Cartesian grids WENO extrapolation hybrid scheme.
Author Details
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Steady-state simulation of Euler equations by the discontinuous Galerkin method with the hybrid limiter
Wei, Lei
Xia, Yinhua
Journal of Computational Physics, Vol. 515 (2024), Iss. P.113288
https://doi.org/10.1016/j.jcp.2024.113288 [Citations: 1]