Numerical solution of natural-convection flow in enclosures: An implicit vorticity boundary condition type method

Abstract

This paper presents a numerical method for solving viscous incompressible Navier-Stokes equations and their application to natural-convection flow. A generalized solution methodology based on the existing vorticity-stream function methods has been developed to show that the vorticity boundary condition being implemented is explicit in nature. A novel two-dimensional numerical solution method of vorticity-stream function formulation is proposed by implementing vorticity boundary conditions implicitly. The developed method is applied to various types of two-dimensional boundaries encountered in natural- convection flows such as: A) regular (square/rectangular) boundary enclosures, b) nonrectangular/irregular boundary enclosures, c) boundary with obstructions. The results obtained match closely with standard reference results available in the literature demonstrating the second-order overall accuracy. Convergence behavior of implicit vorticity boundary conditions shows that the present method exhibits faster convergence and bett er stability over the conventional vorticity-stream function formulation. The present method requires solution of only one Poisson equation per each iteration time step, thus reducing the overall complexity of the algorithm equivalent to solving a heat conduction-type Poisson problem. © 2019 by Begell House, Inc.