Numerical assessment of a class of uniformly stable mixed spectral elements for the Navier–Stokes equations
In 1999, Bernardi and Maday analyzed a new class of mixed spectral elements for the Stokes and the Navier–Stokes equations [Bernardi C, Maday Y. Uniform Inf–Sup condition for the spectral discretization of the Stokes problem. Math Models Meth Appl Sci 1999;3:395–414] where they proved some interesti...
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| Veröffentlicht in: | Computers & fluids 2007-07, Vol.36 (6), p.1137-1148 |
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| creator | Azaı¨ez, Mejdi Ben Belgacem, Faker Escriva, Xavier Fournié, Michel Karimi-Fard, Mohammad |
| description | In 1999, Bernardi and Maday analyzed a new class of mixed spectral elements for the Stokes and the Navier–Stokes equations [Bernardi C, Maday Y. Uniform Inf–Sup condition for the spectral discretization of the Stokes problem. Math Models Meth Appl Sci 1999;3:395–414] where they proved some interesting results like the uniform Inf–Sup condition. The main advantage we see is that applying the Uzawa algorithm to the discrete Stokes system yields a well-conditioned problem on the pressure. Then, the mass matrix preconditioned Conjugate Gradient method PCG used to compute the pressure converges in a number of iterations that is independent of the polynomial degree approximation. This paper presents the “
numerical proofs” of the theoretical predictions on the stability and the accuracy of these spectral methods in mono-domain and multi-domain configurations. |
| doi_str_mv | 10.1016/j.compfluid.2006.10.002 |
| format | Article |
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| subjects | Computational methods in fluid dynamics Exact sciences and technology Fluid dynamics Fundamental areas of phenomenology (including applications) Physics |
| title | Numerical assessment of a class of uniformly stable mixed spectral elements for the Navier–Stokes equations |
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