Convergence Analysis of LU Scheme for the Euler Equations on Unstructured Meshes

The convergence characteristics of the LV scheme for the Euler equations have been investigated by using the Von Neumann stability analysis. The results indicated that the convergence rate is governed by a specific combination of CFD parameters. Based on this insight, it is shown that the convergence characteristics of the LV scheme is not deteriorated at any grid aspect-ratio as long as the local time step is defined based on the parameter combination. The numerical results demonstrated that this time step definition provide a uniform convergence for grid aspect-ratios between one to$1{\times}10^{4}$.