Fully-conservative high-order FR scheme on moving and deforming grids

An appropriate procedure to construct the symmetric conservative metrics is presented in the high-order conservative flux-reconstruction scheme. The present framework enables a direct discretization of the strong conservation form of governing equations without any errors in the freestream preservation and global conservation properties on threedimensionally moving and deforming grids. We show that a straightforward implementation of the symmetric conservative metrics often fails to construct metric polynomials with the same order of a solution polynomial, which severely degrades a numerical accuracy. On the other hand, the symmetric conservative metrics constructed by the appropriate procedure can preserve the freestream solution regardless of the order of shape functions; in addition, 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.