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

The appropriate procedure for constructing the symmetric conservative metric is presented with which both of the freestream preservation and global conservation proper- ties are satisfied in the high-order conservative flux-reconstruction scheme on a threedimensionally-curved moving and deforming grid. A freestream preservation test is con- ducted, where the freestream preservation and global conservation properties were demonstrated. The symmetric conservative metric constructed by the appropriate procedure preserves the freestream with regardless of the order of shape functions, while other metrics cannot always preserve the freestream. Also a convecting vortex is computed on three-dimensional wavy grids for Euler equations, and the vortex is better preserved when the symmetric conservative metric is appropriately constructed, while it is not when the order of the interpolation polynomial for the metrics is smaller than that for the solution polynomial.