A grid-free central scheme for inviscid compressible flows is presented here. The space derivatives in the governing equations are discretized using the least squares minimization of the error in a Taylor series approximation. The discretization is for any arbitrary cloud of points with full stencil support. A new grid-free central scheme is formulated based on convective - pressure splitting using the mid-points of the lines connecting each point to its neighbours for introducing artificial viscosity. The numerical dissipation is reduced due to the modified eigenvalues in the convective - pressure splitting together with a diffusion regulator based on the jump in the Mach number. The results obtained for standard test cases in two dimensions with first and second order accuracy are presented.
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