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 Algorithms The work related to algorithms includes flow solvers and grid generation for incompressible flows. Various research groups have accomplished the following investigations. 1.1 An Explicit Algorithm for Predicting Unsteady Incompressible Viscous Flows in Arbitrary Geometries A numerical method for predicting viscous flows in complex geometries has been developed. Integral mass and momentum conservation equations are deployed and these are discretized into algebraic form through numerical quadrature. The physical domain is divided into a number of non-orthogonal control volumes, which are isoparametrically mapped onto standard rectangular cells. Numerical integration for unsteady momentum equations is performed over such non-orthogonal cells. Compliance of the mass conservation equation and the consequent evolution of correct pressure distribution are accomplished through an iterative correction of pressure and velocity till divergence-free condition is obtained in each cell. The algorithm has been applied on a few test problems, namely, lid-driven square and oblique cavities, developing flows in a rectangular channel and flow over square and circular cylinders placed in rectangular channels. The results exhibit good accuracy and justify the applicability of the algorithm (Mukhopadhyay et al., 1993; Singh et al., 1998). 1.2 An Overlapping Control Volume Method for the Navier-Stokes Equations on Nonstaggered Grids An algorithm, based on the overlapping control volume (OCV) method, for the solution of the steady and unsteady two-dimensional incompressible Navier-Stokes equations in complex geometry has been developed. The primitive variable formulation is solved on a nonstaggered grid arrangement. The momentum interpolation technique circumvents the problem of pressure-velocity decoupling. The accuracy and effectiveness of the method is established by solving five steady state and one unsteady state test problems. The numerical solutions obtained using the technique are in good agreement with the analytical and benchmark solutions available in the literature. On uinform grids, the methods gives second order accuracy for the both diffusion and convection dominated flows (Verma and Eswaran, 1996; Verma and Eswaran, 1997). 1.3 A Finite Volume Method for Navier-Stokes Equations A finite volume formulation has been developed for unsteady Navier-Stokes solution on complex three-dimensional geometries. The formulation has also been generalized for Reynolds averaged Navier-Stokes equations using k-e model. The formulation is designed to solve the governing equations directly on the physical domain without transformation of either domains or equations. The convection and diffusion fluxes are computed in a manner compatible with the use of irregular hexahedral finite volumes. The convective terms have provision for a variable unwinding factor, and the diffusion fluxes are computed in a novel and natural way. The grid used is collocated, with coinciding velocity and pressure nodes. Pressure velocity decoupling is avoided by momentum interpolation. The comparison of results with those in literature is good. The work has been documented as a conference publication and a report (Eswaran and Prakash, 1988; Senthan et al., 1998). ** The references are available in the list of Publications