# Hegedus Aerodynamics

Comparison of ${ϵ}^{\left(\text{2}\right)}$ Formulations for Artificial Dissipation

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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,

$ϵ i + 1 2 , j , k 2 = κ 2 max⁡ ν i + 1 , ν$ The second formulation, which will be labeled "Average Nu", is as follows,

$ϵ i + 1 2 , j , k 2 = κ 2 2 ν i + 1 + ν i$ 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.