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Proper general decomposition (PGD) for the resolution of Navier-Stokes equations

Abstract : In this work, the PGD method will be considered for solving some problems of fluid mechanics by looking for the solution as a sum of tensor product functions. In the first stage, the equations of Stokes and Burgers will be solved. Then, we will solve the Navier-Stokes problem in the case of the lid-driven cavity for different Reynolds numbers (Re = 100, 1000 and 10,000). Finally, the PGD method will be compared to the standard resolution technique, both in terms of CPU time and accuracy.
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Antoine Dumon, Cyrille Allery, Amine Ammar. Proper general decomposition (PGD) for the resolution of Navier-Stokes equations. Journal of Computational Physics, Elsevier, 2011, 230 (4), pp.1387-1407. ⟨10.1016/j.jcp.2010.11.010⟩. ⟨hal-01061383⟩

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