A finite difference solver for incompressible Navier-Stokes flows in complex domains

Modern CFD applications require the treatment of general complex domains to accurately model the emerging flow patterns. In the present work, a new low order finite difference scheme is employed and tested for the numerical solution of the incompressible Navier-Stokes equations in a complex domain described in curvilinear coordinates. A staggered grid discretization is used on both the physical and computational domains. A subgrid based computation of the Jacobian and the metric coefficients of the transformation is used. The incompressibility condition, properly transformed in curvilinear coordinates, is enforced by an iterative procedure employing either a modified local pressure correction technique or the globally defined numerical solution of a general elliptic BVP. Results obtained by the proposed overall solution technique, exhibit very good agreement with other experimental and numerical calculations for a variety of domains and grid configurations. The overall numerical solver effectively treats the general complex domains.