Dynamic solid mechanics using finite volume methods

A procedure for evaluating the dynamic structural response of elastic solid domains is presented. A prerequisite for the analysis of dynamic fluid–structure interaction is the use of a consistent set of finite volume (FV) methods on a single unstructured mesh. This paper describes a three-dimensional (3D) FV, vertex-based method for dynamic solid mechanics. A novel Newmark predictor–corrector implicit scheme was developed to provide time accurate solutions and the scheme was evaluated on a 3D cantilever problem. By employing a small amount of viscous damping, very accurate predictions of the fundamental natural frequency were obtained with respect to both the amplitude and period of oscillation. This scheme has been implemented into the multi-physics modelling software framework, PHYSICA, for later application to full dynamic fluid structure interaction.

A finite-volume shallow layer method for the MHD instabilities in an aluminium production cell

An electrolytic cell for Aluminium production contains molten metal and molten electrolyte, which are subject to high dc-currents and magnetic fields. Lorentz forces arising from the cross product of current and magnetic field may amplify natural gravity waves at the interface between the two fluids, leading to short circuits in extreme cases. The external magnetic field and current distribution in the production cell is computed through a detailed finite element analysis at Torino Polytechnic. The results are then used to compute the magnetohydrodynamic and thermal effects in the aluminium/electrolyte bath. Each cell has lateral dimensions of 6m x 2m, whilst the bath depth is only 30cm. the electrically resistive electrolyte path, which is critical in the operation of the cell, has layer depth of only a few centimetres below each carbon anode. Because the shallow dimensions of the liquid layer a finite-volume shallow-layer technique has been used at Greenwich to compute the resulting flow-field and interface perturbations. The information obtained from this method, i.e. depth averaged velocities and aluminium/electrolyte interface position is then embedded in the three-dimensional finite volume code PHYSICA and will be used to compute the heat transfer and phase change in the cell.