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The use of Stokes' fundamental solution for the boundary only element formulation of the three‐dimensional Navier–Stokes equations for moderate Reynolds numbers
Author(s) -
Power Henry,
Partridge Paul W.
Publication year - 1994
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620371104
Subject(s) - boundary element method , mathematics , mathematical analysis , stokes flow , stokes' law , integral equation , reciprocity (cultural anthropology) , volume integral , hagen–poiseuille flow from the navier–stokes equations , reynolds averaged navier–stokes equations , flow (mathematics) , finite element method , geometry , physics , computational fluid dynamics , mechanics , social psychology , psychology , thermodynamics
This paper presents a boundary element formulation for the permanent Navier–Stokes equations in which the well‐known closed‐form fundamental solution for the steady Stokes equations is employed. In this way, from the integral representation formulae for the Stokes' equations, an integral equation is found in which the original non‐linear convective terms of the Navier–Stokes equations appear as a domain integral. Additionally, the method of dual reciprocity is used to transform the domain integral to boundary integrals (this method is closely related to the method of particular integrals also used in the literature to transform domain integrals to boundary integrals). Numerical results are presented for the three‐dimensional internal flow in a cylindrical container with a rotating cover, in which the accuracy of the method is shown.