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Fundamental solutions of the streamfunction–vorticity formulation of the Navier–Stokes equations
Author(s) -
RodriguezPrada H. A.,
Pironti F. F.,
Sáez A. E.
Publication year - 1990
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.1650100102
Subject(s) - mathematics , discretization , navier–stokes equations , stream function , mathematical analysis , vorticity , partial differential equation , boundary element method , boundary value problem , finite element method , hagen–poiseuille flow from the navier–stokes equations , vortex , physics , mechanics , compressibility , thermodynamics
A new boundary element procedure is developed for the solution of the streamfunction–vorticity formulation of the Navier–Stokes equations in two dimensions. The differential equations are stated in their transient version and then discretized via finite differences with respect to time. In this discretization, the non‐linear inertial terms are evaluated in a previous time step, thus making the scheme explicit with respect to them. In the resulting discretized equations, fundamental solutions that take into account the coupling between the equations are developed by treating the non‐linear terms as in homogeneities. The resulting boundary integral equations are solved by the regular boundary element method, in which the singular points are placed outside the solution domain.