Two different domain decomposition methods are implemented for the parallel solution of the Poisson's equation arising in the numerical analysis of the incompressible flow problems. The Poisson's equation is written both in terms of pressure and auxiliary potential. As a test case, the cubic cavity problem is analysed with both methods and formulations. In light of cavity results, flow about a complex geometry, wing-winglet configuration, is analysed using the more efficient domain decomposition method. Pressure and auxiliary potential formulation solutions are compared in terms of accuracy, computation time and parallel efficiency.