Hegedus Aerodynamics

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Two formulations for ${ϵ}^{\left(\text{2}\right)}$, which is required for artificial dissipation, are compared.

The first formulation, which will be labeled "Maximum Nu", is as follows,

$${ϵ}_{i+\frac{1}{2}\text{,}j\text{,}k}^{\left(\text{2}\right)}={\kappa }^{\left(\text{2}\right)}\max \left\{{\nu }_{i+1}\text{,}\nu \right\}$$ The second formulation, which will be labeled "Average Nu", is as follows,

$${ϵ}_{i+\frac{1}{2}\text{,}j\text{,}k}^{\left(\text{2}\right)}=\frac{{\kappa }^{\left(2\right)}}{2}\left({\nu }_{i+1}+{\nu }_i\right)$$ The following plot shows the convergence of both formulations for a NACA 0012 Euler run at Mach 1.4 and an angle of attack of 4 degrees.

The following contour plot shows the L2 norm of the Δq vector for each grid point for the maximum nu formulation at the last time step.