Abstract
A new least-squares weak form for the Stokes problem is presented. In the proposed formulation, the pressure is separated on the analytical level. It is shown that stability of the separated systems obtained is independent of the Reynolds number, in contrast to the common sensitive coupled or penalty primitive variable formulations. This is achieved for the price of admitting a larger number of variables. The new formulation is particularly suitable when application of operator splitting methods (Bristeau et al. 1985) is considered. It is applicable both to two and to three dimensional situations. Complementary information required for direct implementation to the nonlinear Navier-Stokes problem is given in the appendix.
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Gellert, M., Harbord, R. A stable vorticity-velocity formulation for viscous flow analysis. Computational Mechanics 5, 417–427 (1990). https://doi.org/10.1007/BF01113446
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DOI: https://doi.org/10.1007/BF01113446