  High-order CFD 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 behaviour of FR on
deformed meshes for both the 1D linear advection and the 2D Euler equations is
investigated. The analytical foundation of this work is based on a modified von
Neumann analysis for linearly deformed grids that is presented. The temporal
stability limits for linear advection on such grids are also explored
analytically and numerically, with 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.
