By Angiolo Farina, Axel Klar, Robert M. M. Mattheij, Andro Mikeli´c, Norbert Siedow, Antonio Fasano
This quantity provides a evaluate of complicated technological difficulties within the glass and of the maths concerned. it truly is notable that the sort of doubtless small study quarter is very wealthy and demands an impressively huge number of mathematical equipment, together with numerical simulations of substantial complexity. the issues taken care of listed here are very average of the sector of glass production and canopy a wide spectrum of complementary matters: injection molding by way of numerous thoughts, radiative warmth move in glass, nonisothermal flows and fibre spinning. The e-book can definitely be necessary not just to utilized mathematicians, but in addition to physicists and engineers, who can locate in it an outline of the main complex versions and strategies.
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Extra info for Mathematical Models in the Manufacturing of Glass: C.I.M.E. Summer School, Montecatini Terme, Italy 2008
2 Glass-Air Interfaces A two-phase fluid flow problem is considered, involving the flow of both glass and air. The flow domain Ω is described by the geometry of the mould and hence fixed. On the other hand, the air domain Ωa and the glass domain Ωg are separated by moving interfaces Γi , as depicted in Fig. 4c–d, and therefore change in time. In order to model the two-phase fluid flow problem, the glass-air interfaces have to captured. There are different numerical techniques to deal with the moving interfaces in Mathematical Modelling of Glass Forming Processes 37 two-phase fluid flow problems.
The algorithm is initialised by computing initial values for distance function d in all nodes adjacent to the interface φ −1 (0). A second order accurate initialisation procedure is discussed in . M. Groot et al. are colour marked as orange in Fig. 21a. The proximate nodes are the first nodes to be added to the set of accepted nodes, which contains all nodes of which the corresponding values are accepted as a distance value. The remaining nodes are initially tagged as distant, which are colour marked as black in Fig.
5 s a loss volume of less than 1% is observed, which is a good result. 11%. The volume change can be further reduced by decreasing the time step, improving the mesh quality or by using higher order time discretisation schemes. Good volume conservation is also reported in .