A Hybrid WENO Scheme for Steady Euler Equations in Curved Geometries on Cartesian Grids (Communications in Computational Physics, 2023)
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 Cartesiangrids to achieve uniform high-order accuracy. In this paper, we utilize a fifth-orderfinite difference hybrid WENO scheme to simulate steady Euler equations, and thesame fifth-order WENO extrapolation methods are developed to handle the curvedboundary. 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 transformthe tangential derivatives along the curved solid wall boundary. This hybrid WENOscheme is robust for steady-state convergence and maintains high-order accuracy inthe smooth region even with the solid wall boundary condition. Besides, the essentially non-oscillation property is achieved. The numerical spectral analysis also showsthat this hybrid WENO scheme has low dispersion and dissipation errors. Numericalexamples are presented to validate the high-order accuracy and robust performance ofthe hybrid scheme for steady Euler equations in curved domains with Cartesian grids.