  We present a strong form, meshless point collocation explicit solver for the
numerical solution of the transient, incompressible, viscous Navier-Stokes
(N-S) equations in two dimensions. We numerically solve the governing flow
equations in their stream function-vorticity formulation. We use a uniform
Cartesian embedded grid to represent the flow domain. We compute the spatial
derivatives using the Meshless Point Collocation (MPC) method. We verify the
accuracy of the numerical scheme for commonly-used benchmark problems including
lid-driven cavity flow, flow over a backward-facing step and vortex shedding
behind a cylinder. We have examined the applicability of the proposed scheme by
considering flow cases with complex geometries, such as flow in a duct with
cylindrical obstacles, flow in a bifurcated geometry, and flow past
complex-shaped obstacles. Our method offers high accuracy and excellent
computational efficiency as demonstrated by the verification examples, while
maintaining a stable time step comparable to that used in unconditionally
stable implicit methods.
