Annals of the Assembly for International Heat Transfer Conference 13

ISBN 1-56700-225-0 / CD 1-56700-226-9

Year 2006

M.-J. Ni
University of California, Los Angeles, USA

M. Abdou
University of California, Los Angeles, USA

A general second-order temporal accuracy multi-step formula of projection method is given based on matrix analysis. The general formula includes four-step and three-step projection methods. Some classical second-order projection methods, such as BCG (Bell, Colella, Glaz, J. Comput. Phys., 85, 257), CM (Choi, Moin, J. Comput. Phys., 113, 1-4), can be acquired from this general formula. The famous SIMPLE (Int. J. Heat Mass Trans., 15, 1787-1806) and SIMPLE-type methods, such as SIMPLEC (Van Doormaal, Raithby, Numer. Heat Trans. 7, 147-163), are also special cases of this general formula. A bridge between classical projection method and SIMPLE method is built up, and a four-step SIMPLE method is developed. This multi-step projection formula has been extended to multi-phase flows. Level set method and subcell model have been incorporated with the formula for phase change problems with heat and mass transfer across the interface. The numerical results for unsteady vortex flows, lid-driven cavity flows, direct numerical simulation of turbulence, multi-fluid with and without phase change have been illustrated based on the general projection method with constant coefficient matrix and nonlinear coefficient matrix.

MTH-12 pages DOI: 10.1615/IHTC13.p9.120 Download article

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