A numerical study on the benefit of high order methods is performed. Numerical computations of solutions governed by the Euler equations are performed. The propagation of a vortex convected through an empty domain, computations of steady state solutions around a NACA0012 airfoil and vortex-airfoil interaction are considered. These computations show that high order methods are often required in order to capture the significant flow features, especially for transient problems.
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