Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 199, Issue 1, Pages 355-375Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2004.02.012
Keywords
contravariant; Navier-Stokes equations; time-dependent curvilinear coordinates
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The contravariant form of the Navier-Stokes equations in a fixed curvilinear coordinate system is well known. However, when the curvilinear coordinate system is time-varying, such as when a body-fitted grid is used to compute the flow over a compliant surface, considerable care is needed to handle the momentum term correctly. The present paper derives the complete contravariant form of the Navier-Stokes equations in a time-dependent curvilinear coordinate system from the intrinsic derivative of contravariant vectors in a moving frame. The result is verified via direct transformation. These complete equations are then applied to compute incompressible flow in a 2D channel with prescribed boundary motion, and the significant effect of some terms which are sometimes either overlooked or assumed to be negligible in such a derivation is quantified. (C) 2004 Elsevier Inc. All rights reserved.
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