High-Order Flux Reconstruction on Stretched and Warped Meshes

摘要

High-order computational fluid dynamics is gathering a broadening interest as a future industrial tool, with one such approach being flux reconstruction (FR). However, due to the need to mesh complex geometries if FR is to displace current lower-order methods, FR will likely have to be applied to stretched and warped meshes. Therefore, it is proposed that the analytical and numerical behaviors of FR on deformed meshes for both the one-dimensional linear advection and the two-dimensional Euler equations are investigated. The analytical foundation of this work is based on a modified von Neumann analysis for linearly deformed grids, which is presented. The temporal stability limits for linear advection on such grids are also explored analytically and numerically, with Courant-Friedrichs-Lewy (CFL) limits set out for several Runge-Kutta schemes, with the primary trend being that contracting mesh regions give rise to higher CFL limits, whereas expansion leads to lower CFL limits. Lastly, the benchmarks of FR are compared to finite difference and finite volumes schemes, as are common in industry, with the comparison showing the increased wave propagating ability on warped and stretched meshes, and hence FR's increased resilience to mesh deformation.