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METHOD–OF–LINES SOLUTION OF TIME–DEPENDENT TWO–DIMENSIONAL NAVIER–STOKES EQUATIONS
Author(s) -
OYMAK OLCAY,
SELÇUK NEVÍN
Publication year - 1996
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/(sici)1097-0363(19960915)23:5<455::aid-fld435>3.0.co;2-j
Subject(s) - mathematics , pressure correction method , laminar flow , navier–stokes equations , ordinary differential equation , partial differential equation , poisson's equation , numerical partial differential equations , compressibility , mathematical analysis , collocation method , multigrid method , method of lines , computational fluid dynamics , differential equation , physics , differential algebraic equation , mechanics
A novel approach to the development of a code for the solution of the time‐dependent two‐dimensional Navier–Stokes equations is described. The code involves coupling between the method of lines (MOL) for the solution of partial differential equations and a parabolic algorithm which removes the necessity of iterative solution on pressure and solution of a Poisson‐type equation for the pressure. The code is applied to a test problem involving the solution of transient laminar flow in a short pipe for an incompressible Newtonian fluid. Comparisons show that the MOL solutions are in good agreement with the previously reported values. The proposed method described in this paper demonstrates the ease with which the Navier–Stokes equations can be solved in an accurate manner using sophisticated numerical algorithms for the solution of ordinary differential equations (ODEs).