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A numerical method for 3D viscous incompressible flows using non‐orthogonal grids
Author(s) -
He P.,
Salcudean M.
Publication year - 1994
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.1650180503
Subject(s) - mathematics , laminar flow , mathematical analysis , solver , computational fluid dynamics , coordinate system , compressibility , grid , numerical analysis , geometry , mechanics , mathematical optimization , physics
Abstract This paper presents a numerical method for fluid flow in complex three‐dimensional geometries using a body‐fitted co‐ordinate system. A new second‐order‐accurate scheme for the cross‐derivative terms is proposed to describe the non‐orthogonal components, allowing parts of these terms to be treated implicitly without increasing the number of computational molecules. The physical tangential velocity components resulting from the velocity expansion in the unit tangent vector basis are used as dependent variables in the momentum equations. A coupled equation solver is used in place of the complicated pressure correction equation associated with grid non‐orthogonality. The co‐ordinate‐invariant conservation equations and the physical geometric quantities of control cells are used directly to formulate the numerical scheme, without reference to the co‐ordinate derivatives of transformation. Several two‐ and three‐dimensional laminar flows are computed and compared with other numerical, experimental and analytical results to validate the solution method. Good agreement is obtained in all cases.