  Computational fluid dynamics and aerodynamics, which complement more
expensive empirical approaches, are critical for developing aerospace vehicles.
During the past three decades, computational aerodynamics capability has
improved remarkably, following advances in computer hardware and algorithm
development. However, for complex applications, the demands on computational
fluid dynamics continue to increase in a quest to gain a few percent
improvements in accuracy. Herein, we numerically demonstrate that optimizing
the metric terms which arise from smoothly mapping each cell to a reference
element, lead to a solution whose accuracy is practically never worse and often
noticeably better than the one obtained using the widely adopted Thomas and
Lombard metric terms computation (Geometric conservation law and its
application to flow computations on moving grids, AIAA Journal, 1979). Low and
high-order accurate entropy stable schemes on distorted, high-order tensor
product elements are used to simulate three-dimensional inviscid and viscous
compressible test cases for which an analytical solution is known.
