A finite point method for compressible flow

This is the accepted version of the following article: [Löhner, R. , Sacco, C. , Oñate, E. and Idelsohn, S. (2002), A finite point method for compressible flow. Int. J. Numer. Meth. Engng., 53: 1765-1779. doi:10.1002/nme.334], which has been published in final form at https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.334A weighted least squares finite point method for compressible flow is formulated. Starting from a global cloud of points, local clouds are constructed using a Delaunay technique with a series of tests for the quality of the resulting approximations. The approximation factors for the gradient and the Laplacian of the resulting local clouds are used to derive an edge-based solver that works with approximate Riemann solvers. The results obtained show accuracy comparable to equivalent mesh-based finite volume or finite element techniques, making the present finite point method competitive.Peer Reviewe