Symbolic-numeric implementation of the method of collocations and least squares for 3d navier--stokes equations

Authors:
Vasily P. Shapeev;Evgenii V. Vorozhtsov
Affiliations:
Khristianovich Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, Novosibirsk, Russia;Khristianovich Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, Novosibirsk, Russia
Venue:
CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing
Year:
2012

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Abstract

The method of collocations and least squares, which was previously proposed for the numerical solution of the two-dimensional Navier---Stokes equations governing steady incompressible viscous flows, is extended here for the three-dimensional case. The derivation of the collocation and matching conditions is carried out in symbolic form using the CAS Mathematica. The numerical stages are implemented in a Fortran code, into which the left-hand sides of the collocation and matching equations have been imported from the Mathematica program. The results of numerical tests confirm the second order of convergence of the presented method.