The Development of a Computational Scheme Using Both a Scalar and a Vector Potential : Application to the Buoyant Flow in Two-and Three-Dimensional Fields

Abstract

A computational scheme was developed using both a scalar and a vector potential which was originally proposed by Hirasaki and Hellums and was recently rephrased by Richardson and Cornish on the boundary conditions in detail. This equation system has not been apparently employed for numerical calculation so far but herein was applied to a number of cases of flow. Isothermal two-dimensional flow through a square box with openings at R_e=81.6 was studied. Computed velocity field agreed very well with the results obtained by a classical way of stream function whose gradient is given at the opening for a plug flow. Two-dimensional steady mixed convection and three-dimensional unsteady buoyant flow were further studied and found to give a stable solution.