A new higher-order finite volume method based on Moving Least Squares for the resolution of the incompressible Navier–Stokes equations on unstructured grids

In this work a new higher-order ( > 2) accurate finite volume method for the resolution of the incompressible Navier–Stokes equations on unstructured grids is presented. The formulation is based on the use of Moving Least Squares (MLS) approximants. Third and fourth order accurate discretizations of the convective and viscous fluxes are obtained on collocated meshes. In addition, MLS is employed to design a new Momentum Interpolation Method that allows interpolations better than linear on any kind of mesh. The accuracy and performance of the proposed method is demonstrated by solving different steady and unsteady benchmark problems on unstructured grids.