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A finite element method to solve the Navier‐Stokes equations using the method of characteristics
Author(s) -
Huffenus J. P.,
Khaletzky D.
Publication year - 1984
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/fld.1650040304
Subject(s) - upwind scheme , mathematics , laminar flow , poisson's equation , finite element method , interpolation (computer graphics) , pressure correction method , navier–stokes equations , computational fluid dynamics , mathematical analysis , mechanics , frame (networking) , computer science , physics , discretization , telecommunications , compressibility , thermodynamics
We present a simple and efficient finite element method to solve the Navier‐Stokes equations in primitive variables V, p. It uses (a) an explicit advection step, by upwind differencing. Improvement with regard to the classical upwind differencing scheme of the first order is realized by accurate calculation of the characteristic curve across several elements, and higher order interpolation; (b) an implicit diffusion step, avoiding any theoretical limitation on the time increment, and (c) determination of the pressure field by solving the Poisson equation. Two laminar flow calculations are presented and compared to available numerical and experimental results.