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This paper is concerned with the development of a high-order upwind conservative numerical method for the simulation of flows of a Newtonian fluid. The domain is discretised using a Cartesian grid from which non-overlapping rectangular control-volumes are formed.\udLine integrals arising from the integration of the diffusion and convection terms over control volumes are evaluated using the middle-point rule. The diffusion term is approximated using two different schemes, namely one-dimensional integrated radial basis function networks (1D-IRBFN) and central differences. The convection term is effectively treated by a high-order upwind scheme incorporating 1D-IRBFNs with the deferred-correction strategy. Several test problems governed by the Burgers and the Navier-Stokes equations are simulated, which show\udthat the proposed technique is stable, accurate and converges well

An upwind control-volume method based on integrated RBFs for fluid-flow problems