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AN APPROXIMATE PROJECTION SCHEME FOR INCOMPRESSIBLE FLOW USING SPECTRAL ELEMENTS
Author(s) -
TIMMERMANS L. J. P.,
MINEV P. D.,
VAN DE VOSSE F. N.
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(19960415)22:7<673::aid-fld373>3.0.co;2-o
Subject(s) - discretization , pressure correction method , laminar flow , mathematics , incompressible flow , projection method , projection (relational algebra) , compressibility , flow (mathematics) , navier–stokes equations , mass matrix , mathematical analysis , mathematical optimization , dykstra's projection algorithm , algorithm , geometry , mechanics , physics , nuclear physics , neutrino
An approximate projection scheme based on the pressure correction method is proposed to solve the Navier–Stokes equations for incompressible flow. The algorithm is applied to the continuous equations; however, there are no problems concerning the choice of boundary conditions of the pressure step. The resulting velocity and pressure are consistent with the original system. For the spatial discretization a high‐order spectral element method is chosen. The high‐order accuracy allows the use of a diagonal mass matrix, resulting in a very efficient algorithm. The properties of the scheme are extensively tested by means of an analytical test example. The scheme is further validated by simulating the laminar flow over a backward‐facing step.