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

作　　者：Yifei Wan Yinhua Xia 

机构地区：[1]School of Mathematical Sciences,University of Science and Technology of China,Hefei,Anhui 230026,P.R.China

出　　处：《Communications in Computational Physics》2023年第5期1270-1331,共62页计算物理通讯（英文）

基　　金：Research supported by NSFC grant No.12271498;National Key R&D Program of China No.2022YFA1005202/2022YFA1005200.

摘　　要：For steady Euler equations in complex boundary domains,high-order shockcapturing 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.

关 键 词：Euler equations steady-state convergence curved boundary Cartesian grids WENO extrapolation hybrid scheme 

分 类 号：O175[理学—数学]