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A coupled heat and fluid flow, stresses and deformation modelling tool including macrosegregation and inter-dendritic flows have been developed for various semi-continuous or batch casting processes in use by the light metal industries. Results from the mechanical calculation are back-coupled to the thermal boundary conditions regarding size of contact zones and air-gaps and thereby enabling automatic calculation of gap dependent heat transfer coefficients, which is very useful for the industrial use of the tool. Examples from the application of the model on direct chill castings are made, as well as on twin roll, wheel and belt and chain conveyor casting. Comparison with measurements and other process data are done. The finite element method is used for the modelling tool including dynamic treatment of elements in moving parts of the calculation domains. In continuous casting there are frequently interfaces where the metal slides against the equipment, and although the grid across such surfaces does not match they are still coupled implicitly in Alsim. This adds an ability to model complex processes involving stresses and deformations in mechanical coupled moving parts and it alleviates the time consuming process of producing the initial finite element grids for the geometries. In order to handle solidification phenomena like hot-tearing, macrosegregation and exudation local adaptive grid refinement is necessary, as well as parallelization of the code, to achieve acceptable accuracies. How these numerical challenges are handled in the model is described.

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A novel nonintrusive reduced-order modeling approach is proposed for parametrized unsteady flow and heat transfer problems. A set of reduced basis functions are extracted via a proper orthogonal decomposition (POD) method from a collection of high-fidelity numerical solutions (snapshots of spatial distribution at a series of time steps) that are computed for properly chosen parameters (e.g., material property, initial/boundary conditions) using a full-order model (finite-volume/finite-element methods). Here, the time dimension is treated separately from other parameters, reflecting the dynamic features of the flow problems. Dynamic mode decomposition is used to decompose the time-resolved data (POD coefficients) into dynamics modes and reconstruct/predict the dynamic evolution of the flow systems. The POD coefficients at every time step under the condition of a set of parameters are approximated through interpolation with the radial basis function method from those obtained from the snapshots of the chosen parameter space. Hence, the POD coefficients at a set of given time and parameters can be approximated, and the spatial distribution of the solution data can be reconstructed. The current reduced-order model has been applied to the problems governed by a set of parametrized unsteady Navier-Stokes and heat conduction equations. The model capability has been illustrated numerically by three numerical test cases: flow past a cylinder, melt solidification, and dam break. The model prediction capabilities have been evaluated by varying the material properties (viscosity and density) and the heat transfer conditions on some of the boundaries. An error analysis is also carried out to show the model prediction accuracy.

A neural network architecture called ART2/BP is proposed. Thc goal has been to construct an artificial neural network that learns incrementally an unknown mapping, and is motivated by the instability found in back propagation (BP) networks: after first learning pattern A and then pattern B, a BP network often has completely 'forgotten' pattern A. A network using both supervised and unsupervised training is proposed, consisting of a combination of ART2 and BP. ART2 is used to build and focus a supervised backpropagation network consisting of many small subnetworks each specialized on a particular domain of the input space. The ART2/BP network has the advantage of being able to dynamically expand itself in response to input patterns containing new information. Simulation results show that the ART2/BP network outperforms a classical maximum likelihood method for the estimation of a discrete dynamic and nonlinear transfer function

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