| A mesh adaptation procedure is presented to capture vortices in a numerical calculation. The error estimator of the adaptation scheme is based on the Hessian of a scalar field. To make convergence faster toward the analytic solution, a new scalar field is introduced: a transported vorticity. This field is computed as a separate equation in the solver, therefore having no influence on the flow computation. The sum of the original vorticity and the transported vorticity is used to calculate the Hessian. This method allows a better vortex capture farther downstream in the axial direction. To assess the quality of the proposed methodology, a simple test case without any lifting foil is first studied. An analytic vortex is set at the inlet of a rectangular cross-section tunnel and expands downstream. Results obtained with hexahedral elements are compared to results obtained with tetrahedral elements. In a second test case, the analytic vortex is replaced by a hydrofoil from which a tip vortex is created. Numerical velocity profiles are compared with experimental results. |
