High-order simulations of isothermal flows using the local anisotropic basis function method (LABFM)

Mesh-free methods have significant potential for simulations of flows in complex geometries, with the difficulties domain discretisation greatly reduced. However, many mesh-free are limited to low order accuracy. In compete conventional mesh-based methods, high accuracy is essential. The Local Anisotropic Basis Function Method (LABFM) a method introduced King et al. (2020) [20], which enables construction highly accurate difference operators on disordered node discretisations. Here, we introduce number developments LABFM, areas basis function construction, stencil optimisation, stabilisation, variable resolution, and boundary conditions. With these developments, direct numerical Navier Stokes equations possible at extremely (up 10th characteristic spacing internally). We numerically solve isothermal compressible range geometries: periodic channel flows, past cylinder, porous media. Excellent agreement seen analytical solutions, published results (using spectral element method), experiments. geometries demonstrated subsonic transonic through an inhomogeneous media pore Reynolds numbers up Rep=968.