High-order consistent SPH with the pressure projection method in 2-D and 3-D

•A novel high-order accurate incompressible SPH formulation is presented.•High-order consistency enforced ensuring uninhibited SPH spatial error convergence.•Hybrid technique combines high-order smoothing accuracy and second-order consistency.•Stabilising techniques proposed for collocated projection method based high-order SPH.•2-D/3-D tests validate accuracy and robustness of the proposed high-order SPH scheme.