|Numerical investigation of three-dimensional separation in a forward-facing step flow using a spectral element method
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|In this study, high-resolution simulations of the flow over a forward-facing step (FFS) are presented. The simulations are performed using a spectral element code that combines high accuracy with geometric flexibility. Concerning this numerical approach, it is shown that for the PN - PN -2 spectral element method, in which velocity and pressure are approximated by polynomials of order N and N 2, respectively, numerical instabilities can occur, depending on the formulation of the nonlinear term. An eigenvalue analysis of the fully discretized system clearly shows that the spatial discretization is stable for the convective form but unstable for the divergence, the skew-symmetric, and the standard rotational forms. It is demonstrated that the instability is related to the divergence error of the computed solution in the velocity points where continuity is not enforced. In spectral element simulations, usually most of the computing time is spent on the solution of the pressure equation. Therefore, an efficient direct solver which is applicable whenever the flow domain can be decomposed into Cartesian subdomains has been developed. Our simulations of the three-dimensional FFS flow are adjusted to the configuration considered in a recent experiment. Comparison with the experimental results shows good agreement of the flow topology in the step region and of the spanwise spacing of the characteristic streaks that form downstream of the step. It is demonstrated in the present work that the three-dimensionality of the FFS flow is not induced by an absolute instability, which was suggested previously in the literature. Rather, it is caused by disturbances present in the oncoming flow to which the flow in the step region reacts very sensitively. Furthermore, a smooth transition from an almost two-dimensional to a fully three-dimensional state is observed if the disturbance level is gradually increased. Consequently, under the considered conditions, no critical threshold below which the flow remains two-dimensional is found.
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Wilhelm, D. (2000). Numerical investigation of three-dimensional separation in a forward-facing step flow using a spectral element method [Doctoral dissertation, ETH Zürich]. https://doi.org/10.3929/ethz-a-004037003
Wilhelm, D. (2000) Numerical investigation of three-dimensional separation in a forward-facing step flow using a spectral element method. Doctoral dissertation. ETH Zürich. Available at: https://doi.org/10.3929/ethz-a-004037003.
D. Wilhelm, “Numerical investigation of three-dimensional separation in a forward-facing step flow using a spectral element method,” Doctoral dissertation, ETH Zürich, 2000. doi: 10.3929/ethz-a-004037003.
Wilhelm, Dirk. Numerical Investigation of Three-Dimensional Separation in a Forward-Facing Step Flow Using a Spectral Element Method. ETH Zürich, 2000, https://doi.org/10.3929/ethz-a-004037003.
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