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Augmented Lagrangian technique applied to a spatially periodic, harmonic Navier‐Stokes problem
Author(s) -
Borne Lionel
Publication year - 1987
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.1650070605
Subject(s) - augmented lagrangian method , computation , simple (philosophy) , mathematics , finite element method , lagrangian , harmonic , simple harmonic motion , mathematical optimization , algorithm , classical mechanics , physics , philosophy , epistemology , quantum mechanics , thermodynamics
An application and an extension (to complex variables) of the classical augmented Lagrangian method is performed. Finite element computations are realized in the two‐dimensional case of an harmonic Navier‐Stokes problem with periodic boundary conditions. A formulation (extended from the traditional Stokes problem) involving a simple Lagrangian, solved by the Uzawa algorithim, was previously used. 1 This treatment proved unsatisfactory for large frequencies. The efficient and well‐known augmented Lagrangian technique solved by the Uzawa algorithm is used to overcome these shortcomings. Other, better techniques could be used. Nevertheless the simple method used here is efficient. Moreover the numerical implementation needs little memory storage, which is an important factor in this particular case. The well‐known conditioning technique employed is shown to be well‐adapted in this case, a fact which emerges from the study of the non‐symmetric problem involved. Finally, many tests, computations and experimental data are presented.