A Hybrid WENO Scheme for Steady Euler Equations in Curved Geometries on Cartesian Grids

A Hybrid WENO Scheme for Steady Euler Equations in Curved Geometries on Cartesian Grids

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

Yifei Wan

Yinhua Xia

  1. 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]