A new Mean Preserving Moving Least Squares method for Arbitrary Order Finite Volume schemes

In this paper we propose a new arbitrary-order Finite Volume method for the numerical solution of Euler and Navier-Stokes equations on unstructured grids. Arbitrary order is achieved using modified Moving Least Squares reconstruction, which preserves mean values conservative variables. Hence, proposed scheme changes traditional error functional MLS reconstruction in to compare cell-averaged values. Several benchmark problems are used assess scheme’s accuracy performance, show that arbitrary convergence can be achieved. Furthermore, applied its ability simulate turbulent flows verified.