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Projection method for flows with large local density gradients: Application to dendritic solidification
Author(s) -
Heinrich J. C.,
Sajja U. K.,
Felicelli S. D.,
Westra D. G.
Publication year - 2008
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.1812
Subject(s) - projection (relational algebra) , polygon mesh , work (physics) , momentum (technical analysis) , coupling (piping) , projection method , mechanics , directional solidification , range (aeronautics) , geology , computer science , materials science , mathematical optimization , physics , mathematics , geometry , thermodynamics , algorithm , dykstra's projection algorithm , alloy , metallurgy , finance , composite material , economics
Numerical models of solidification including a mushy zone are notoriously inefficient; most of them are based on formulations that require the coupled solution to the velocity components in the momentum equation greatly restricting the range of applicability of the models. Initial attempts at modeling directional solidification in the presence of a developing mushy zone using a projection formulation encountered difficulties once solidification starts, which were traced to the inability of the method to deal with large local density differences in the vicinity of the fluid–mush interface. A modified formulation of the projection method has been developed that maintains the coupling between the body force and the pressure gradient and is presented in this work. This formulation is shown to be robust and extremely efficient; reducing very significantly the necessary storage and the computational time required for the simulation of problems involving very large meshes when compared with previously published data. This is illustrated in this work through its application to simulations involving a Pb–Sn alloy. Copyright © 2008 John Wiley & Sons, Ltd.