Purpose - The purpose of this paper is to present two low diffusive convective-pressure flux split finite volume algorithms for solving incompressible flows in artificial compressibility framework. Design/methodology/approach - The present method follows the framework similar to advection upwind splitting method of Liou and Steffen for compressible flows which is used by Vierendeels et al. to solve incompressible flow equations. Instead of discretizing the total inviscid flux using upwind scheme, the inviscid flux is first split into convective and pressure parts, and then discretized the two parts differently. The convective part is discretized using upwind method and the pressure part using central differencing. Since the Vierendeels type scheme may not be able to capture the divergence free velocity field due to the presence of artificial dissipation term, a strategy to progressively withdraw the dissipation with time step is proposed here that can ascertain the divergence free velocity condition to the level of residual error. This approach helps in reducing the amount of numerical dissipation due to upwind discretization, which is evident from the numerical test examples. Findings - Upwind treatment of only the convective part of the inviscid flux terms, instead of the whole inviscid flux term, leads to more accurate solutions even at relatively coarse grids, which is substantiated by numerical test examples. Research limitations/implications - The method is presently applicable to Cartesian grid. Originality/value - Although similar formulation is reported by Vierendeels et al., no detailed study of the accuracy is presented. Discretization and solution reconstructions used in the present approach differ from the approach reported by Vierendeels et al. A modification to Vierendeels type scheme is proposed that can help in achieving divergence free velocity condition. Finally the efficacy of the present approach to produce very accurate solutions even on coarse grids is successfully demonstrated using a few benchmark problems.