Conservative high-order flux-reconstruction schemes on moving and deforming grids

An appropriate procedure to construct symmetric conservative metrics is presented for the high-order conservative flux-reconstruction scheme on three-dimensionally moving and deforming grids. The present framework enables direct discretization of the strong conservation form of governing equations without any errors in the freestream preservation and global conservation properties. We demonstrate that a straightforward implementation of the symmetric conservative metrics often fails to construct metric polynomials having the same order as a solution polynomial, which severely degrades the numerical accuracy. On the other hand, the symmetric conservative metrics constructed using an appropriate procedure can preserve the freestream solution regardless of the order of shape functions. Moreover, a convecting vortex is more accurately computed on deforming grids. The global conservation property is also demonstrated numerically for the convecting vortex on deforming grids.