Three-dimensional free surface modelling in an unstructured mesh environment for metal processing applications

In the casting of metals, tundish flow, welding, converters, and other metal processing applications, the behaviour of the fluid surface is important. In aluminium alloys, for example, oxides formed on the surface may be drawn into the body of the melt where they act as faults in the solidified product affecting cast quality. For this reason, accurate description of wave behaviour, air entrapment, and other effects need to be modelled, in the presence of heat transfer and possibly phase change. The authors have developed a single-phase algorithm for modelling this problem. The Scalar Equation Algorithm (SEA) (see Refs. 1 and 2), enables the transport of the property discontinuity representing the free surface through a fixed grid. An extension of this method to unstructured mesh codes is presented here, together with validation. The new method employs a TVD flux limiter in conjunction with a ray-tracing algorithm, to ensure a sharp bound interface. Applications of the method are in the filling and emptying of mould cavities, with heat transfer and phase change.

A semi-Lagrangian finite volume method for solving viscoelastic flow problems

Recently, there has been considerable interest in solving viscoelastic problems in 3D particularly with the improvement in modern computing power. In many applications the emphasis has been on economical algorithms which can cope with the extra complexity that the third dimension brings. Storage and computer time are of the essence. The advantage of the finite volume formulation is that a large amount of memory space is not required. Iterative methods rather than direct methods can be used to solve the resulting linear systems efficiently.