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CBOS Finite Element Method for Two-Sided Non-Facing LID-Driven Square Cavity Flows

Author(s): Qingxiang Shui; Daguo Wang; Bing Xu

Linked Author(s): Bing Xu

Keywords: Characteristic-based operator-splitting (CBOS); Finite element method; Two-sided non-facing square cavity

Abstract: The characteristic-based operator-splitting (CBOS) finite element method is extended to two-dimensional incompressible viscous flow in the two-sided non-facing lid-driven square cavity. In each time step, the Navier-Stokes (N-S) equations are split into the diffusive term, the convective term and the pressure term by adopting operator-splitting method. For the diffusive term and the pressure term, the temporal discretization is based on backward difference method and the spatial discretization is performed by the standard Galerkin method. The results of the diffusive term are used as the initial values of the convective term. The convective term is a hyperbolic equation and also solved explicitly. The simple explicit characteristic temporal discretization, which involves a local Taylor expansion, is referenced from the CBS algorithm and applied to the discretization of the convective term. The CBOS-based code is validated by simulating one-sided lid-driven square cavity flows. The present algorithm results agree excellent with Ghia’s data. Then, the present algorithm is used to simulate the two-sided non-facing lid-driven square cavity flows at Reynolds numbers100, 1000 and 1071 on a 60×60 mesh. The numerical results imply that the CBOS finite element method is accurate for incompressible viscous flow and holds very good promise in computational fluid dynamics.


Year: 2013

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