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A COMPARATIVE STUDY OF TIME‐STEPPING TECHNIQUES FOR THE INCOMPRESSIBLE NAVIER‐STOKES EQUATIONS: FROM FULLY IMPLICIT NON‐LINEAR SCHEMES TO SEMI‐IMPLICIT PROJECTION METHODS
Author(s) -
TUREK STEFAN
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(19960530)22:10<987::aid-fld394>3.0.co;2-7
Subject(s) - discretization , mathematics , projection method , projection (relational algebra) , navier–stokes equations , euler equations , finite volume method , nonlinear system , finite difference , backward euler method , pressure correction method , compressibility , mathematical analysis , mathematical optimization , algorithm , dykstra's projection algorithm , physics , quantum mechanics , mechanics , engineering , aerospace engineering
Abstract We present a numerical comparison of some time‐stepping schemes for the discretization and solution of the non‐stationary incompressible Navier– Stokes equations. The spatial discretization is by non‐conforming quadrilateral finite elements which satisfy the LBB condition. The major focus is on the differences in accuracy and efficiency between the backward Euler, Crank–Nicolson and fractional‐step Θ schemes used in discretizing the momentum equations. Further, the differences between fully coupled solvers and operator‐splitting techniques (projection methods) and the influence of the treatment of the nonlinear advection term are considered. The combination of both discrete projection schemes and non‐conforming finite elements allows the comparison of schemes which are representative for many methods used in practice. On Cartesian grids this approach encompasses some well‐known staggered grid finite difference discretizations too. The results which are obtained for several typical flow problems are thought to be representative and should be helpful for a fair rating of solution schemes, particularly in long‐time simulations.