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Abstract: The subject of the paper is the numerical simulation of the interaction of two-dimensional incompressible viscous flow and a vibrating airfoil with large amplitudes. A solid airfoil with three degrees of freedom performs rotation around an elastic axis, oscillations in the vertical direction and rotation of a flap. The numerical simulation consists of the finite element solution of the Navier–Stokes equations coupled with a system of nonlinear ordinary differential equations describing the airfoil motion. The time-dependent computational domain and a moving grid are treated by the arbitrary Lagrangian–Eulerian (ALE) formulation of the Navier–Stokes equations. High Reynolds numbers require the application of a suitable stabilization of the finite element discretization. With the aid of numerical experiments we analyze the convergence of the method, if the computational mesh is refined and the time step is successively decreased. Also the effect of the loose (weak) and strong coupling of the flow and structure problems is tested. The applicability of the method is demonstrated by the comparison with NASTRAN computations and the solution of the coupled fluid–structure problem with increasing far-field velocity up to and behind the flutter instability. The developed method can be used in theoretical prediction of dynamic behaviour of aeroelastic systems especially when the system stability has been lost. [Copyright &y& Elsevier]

Abstract: Simulation of shape casting processes involves the simultaneous capture of the rapidly developing metal–air free surface and the liquid–solid moving boundary in the metal phase. Although a wide range of techniques have been developed to address this problem, there are occasions where existing techniques are limited, especially in very complex geometries where the mesh quality may inevitably be relatively poor at some key locations. Cell-centred finite volume methods, typical of most commercial CFD tools, are computationally efficient, but can lead to convergence problems on meshes that feature cells with highly non-orthogonal shapes. The control volume–finite element method uses a vertex-based approach and handles distorted meshes with relative ease, but is computationally expensive. A combined vertex-based–cell-centre technique, described in this paper, solves the flow field at the cell or element vertex, and all other variables are solved at the cell centre (as in conventional CFD tools). This flow solver strategy is much more tolerant of meshes with poor quality elements, allowing solutions on distorted meshes where purely cell-centred solutions procedures fail. The combined method enables the solution of simultaneous free surface flows coupled with solidification in very complex meshes, thus enabling the capture of such behavior in arbitrarily complex geometrical structures. It is relatively straightforward to embed within generic CC based CFD tools allowing it to be employed in a wide variety of processing applications. [Copyright &y& Elsevier]