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Spline‐blended approximation of Hartmann's flow
Author(s) -
Gheri G.,
Cella A.
Publication year - 1974
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.1620080309
Subject(s) - mathematics , spline interpolation , spline (mechanical) , mathematical analysis , interpolation (computer graphics) , boundary value problem , flow (mathematics) , box spline , smoothing spline , geometry , motion (physics) , classical mechanics , bilinear interpolation , physics , statistics , thermodynamics
The steady state flow problem known in magnetohydrodynamics as Hartmann's flow is converted into variational formulation and is given an approximate solution by means of the spline blended interpolation technique. The equations of motion consist of two coupled potential flow problems with homogeneous boundary conditions. The spline blended interpolation method is reduced here, because of the shape of the domain, to a cartesian product of cardinal splines with trigonometric or ordinary polynomials. ‘Exact’ boundary conditions are presented by the blending technique. The numerical results indicate that high accuracy is possible with relatively few unknowns.