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Institute for Materials Research

Solidification modelling

Research on Solidification Modelling is focused around the prediction of grain structure using the phase-field method and is undertaken in support of the experimental research on rapid solidification processing. The application of phase-field modelling to rapid solidification poses particular modelling challenges, as the rapid evolution of latent heat means that the system cannot be approximated as isothermal, as is the case for say conventional casting. As the ratio of the thermal diffusivity to the solute diffusivity (known as the Lewis number) is typically 10,000 in most liquid metals, this leads to severe multi-scale challenges.

To deal with such multi-scale problems we have applied a range of advanced numerical techniques, such as dynamic mesh adaptivity, implicit time-stepping and a non-linear multigrid solver to phase-field modes that solve for the coupled diffusion of both heat and solute in 2- and 3- dimension. In addition, our 3-dimensional code employs parallel processing with dynamic load balancing in order to take advantage of High Performance Computing (HPC) facilities. Both the 2- and 3-dimensional models are formulated in the ‘thin-interface’ limit and as such are capable of yielding quantitatively correct results. Some examples of simulated dendrite morphologies, and the meshes used to perform the simulations, are shown below.

Phase 1Phase 2
Example of a growing dendrite and an adapting mesh in 2-dimensions.

The 2-dimensional code, PhAIM-2d (Phase-field by Adaptive Implicit Multigrid in 2-dimensions) used to generate the simulations above is available as an Open Source download from the Leeds software repository.

PhAIM-2d was developed in c and should run on most Linux machines supporting the Atlas and Blas libraries. The open-source package is freely available for any non-commercial purpose. The 3-dimensional version will be released as an Open Source package when development, debugging and validation work is complete.

Academic Staff
Prof. A.M. Mullis

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