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This study focuses on the derivation of a two-stage pseudo-transient pressuremomentum coupling algorithm for solving incompressible flow problems. The proposed two-stage formulation has been derived from Chorin’s parabolic/elliptic type Fractional-Step Pressure-Projection (FS-PP) method by introducing a pseudotransient pressure term into the second-order pressure-Poisson equation. In other words, the elliptic pressure-Poisson equation has been extended further to a parabolic pressure equation which is directly coupled with the incompressible Navier-Stokes equations for solving stationary laminar flow problems. A benchmark problem of a laminar flow in a two-dimensional microfluidic channel at low Reynolds numbers has been investigated in which case an analytical solution is available for the fully-developed velocity distribution at the outlet. The obtained computational results indicate that the continuity equation for incompressible flows can be satisfied through the proposed pressure-momentum coupling algorithm.

A Pseudo-Transient Pressure-Momentum Coupling Method for Low-Speed Incompressible Flows