Keywords: Navier-Stokes equation, local numerical method, meshless, local pressure-velocity coupling, diffuse approximate method, artificial compressibility method, complex geometry, fluid-flow, parallel, computational fluid dynamics.

A solution for incompressible Navier-Stokes flow in an arbitrary domain is presented in this paper. The solution procedure comprises a variant of the local meshless diffuse approximate method for spatial discretization, explicit time stepping, local pressure-velocity coupling and a simple algorithm for positioning of computational nodes that is based entirely on derivatives of the approximation weight functions. In the proposed numerical methodology the spatial discretization and positioning of computational nodes are solved locally, therefore all algorithms can be effectively executed in parallel without any kind of special treatment of the code. The presented numerical methodology is demonstrated by solving a lid-driven cavity flow problem, where computational domain is filled with random obstacles. The algorithms presented do not require any kind of user input for treating such problems. It is demonstrated that with the solution procedure presented, the fluid flow problem on complex geometries can be efficiently solved.

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