Simulation of laminar flow inside ducts of irregular geometry using integral transforms

Abstract

The Generalized Integral Transform Technique is employed in the hybrid numerical-analytical solution of the steady two-dimensional Navier-Stokes equations, defined within arbitrarily shaped domains, for incompressible laminar channel flow. The formalism is illustrated for the classical test-case of laminar flow in a gradual expansion duct. Numerical results with automatic global accuracy control are obtained for suggested values of Reynolds numbers in the literature, and critically compared against previously reported benchmark solutions for the same problem. The relative merits of the proposed approach are then pointed out.