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A control volume finite difference method for buoyant flow in three‐dimensional curvilinear non‐orthogonal co‐ordinates
Author(s) -
Yang H. Q.,
Yang K. T.,
Lloyd J. R.
Publication year - 1990
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650100206
Subject(s) - curvilinear coordinates , control volume , ordinate , finite volume method , mechanics , flow (mathematics) , mathematics , computational fluid dynamics , geometry , mathematical analysis , physics
This paper presents a control‐volume‐based finite difference method in non‐orthogonal curvilinear coordinates on a local basis in which the vectors and tensors are all based on the general curvilinear coordinates for buoyant flow calculations in arbitrary three‐dimensional geometries. The governing equations are transformed from Cartesian co‐ordinates into generalized curvilinear co‐ordinates. After integrating the set of equations for the control volumes, the finite difference equations are then formulated by a proper treatment of the heat flux and stress tensors and by incorporating the QUICK scheme for the convective terms. The solution procedure then follows the one for three‐dimensional Cartesian co‐ordinates. Examples are given in problems of natural convection in such three‐dimensional enclosures as parallelepiped enclosures and horizontal closed cylinders with differentially heated ends. In the latter case, important applications have been found in crystal growth by means of chemical vapour deposition in a cylindrical ampoule, in which uniform heat fluxes along the two ends are required in order to produce high‐quality crystals. Special attention is given to the insertion of baffles in the cylinder to improve the recirculating flow patterns near the two ends.