A new mixed basis Navier–Stokes formulation for incompressible flows over complex geometries
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Numerical modeling of complex geometries necessitates the use of curvilinear body fitted coordinates. This article proposes a novel mixed basis formulation of the governing conservation equations for general curvilinear non-orthogonal grids with the physical covariant velocity as the primary solution variable. This results in an algorithm which has many advantages of orthogonal equations. The conservation equations written in this form retains the diagonal dominance of the pressure equation. The newly formed conservation equations are solved on a structured grid using the SIMPLER algorithm and are shown to converge well for non-orthogonal grids. Standard K–ϵ model is used for the turbulence closure.
NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Computational Physics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Computational Physics, 307, February 15 (2016), doi: 10.1016/j.jcp.2015.11.065.