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The Lagrangian approach of advective term treatment and its application to the solution of Navier—Stokes equations
Author(s) -
Huffenus J. P.,
Khaletzky D.
Publication year - 1981
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.1650010407
Subject(s) - advection , mathematics , eulerian path , interpolation (computer graphics) , laminar flow , term (time) , stability (learning theory) , numerical diffusion , upwind scheme , convection–diffusion equation , flow (mathematics) , lagrangian , mathematical analysis , mechanics , computer science , classical mechanics , geometry , physics , motion (physics) , discretization , quantum mechanics , thermodynamics , machine learning
A one‐dimensional transport test applied to some conventional advective Eulerian schemes shows that linear stability analyses do not guarantee the actual performances of these schemes. When adopting the Lagrangian approach, the main problem raised in the numerical treatment of advective terms is a problem of interpolation or restitution of the transported function shape from discrete data. Several interpolation methods are tested. Some of them give excellent results and these methods are then extended to multi‐dimensional cases. The Lagrangian formulation of the advection term permits an easy solution to the Navier‐Stokes equations in primitive variables V , p , by a finite difference scheme, explicit in advection and implicit in diffusion. As an illustration steady state laminar flow behind a sudden enlargement is analysed using an upwind differencing scheme and a Lagrangian scheme. The importance of the choice of the advective scheme in computer programs for industrial application is clearly apparent in this example.