arrow
Volume 33, Issue 5
A Hybrid WENO Scheme for Steady Euler Equations in Curved Geometries on Cartesian Grids

Yifei Wan & Yinhua Xia

Commun. Comput. Phys., 33 (2023), pp. 1270-1331.

Published online: 2023-06

Export citation
  • 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.

  • AMS Subject Headings

65N06, 35L65, 76M20

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CiCP-33-1270, author = {Wan , Yifei and Xia , Yinhua}, 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 = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2022-0270}, url = {http://global-sci.org/intro/article_detail/cicp/21762.html} }
TY - JOUR T1 - A Hybrid WENO Scheme for Steady Euler Equations in Curved Geometries on Cartesian Grids AU - Wan , Yifei AU - Xia , Yinhua JO - Communications in Computational Physics VL - 5 SP - 1270 EP - 1331 PY - 2023 DA - 2023/06 SN - 33 DO - http://doi.org/10.4208/cicp.OA-2022-0270 UR - https://global-sci.org/intro/article_detail/cicp/21762.html KW - Euler equations, steady-state convergence, curved boundary, Cartesian grids, WENO extrapolation, hybrid scheme. AB -

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.

Wan , Yifei and Xia , Yinhua. (2023). A Hybrid WENO Scheme for Steady Euler Equations in Curved Geometries on Cartesian Grids. Communications in Computational Physics. 33 (5). 1270-1331. doi:10.4208/cicp.OA-2022-0270
Copy to clipboard
The citation has been copied to your clipboard