Professor Eckart Schnack of Karlsruhe Institute of Technology in Germany recently visited WIT, where he gave a lecture entitled “The Ginzburg-Landau Equation for SiC/SiC-Composites”.
Professor Schnack is a frequent visitor to Ashurst Lodge and his presentations are always followed with great interest. He is particularly renowned for his work on Silicon Carbide products, including the composite of fibres and matrix of this material.
Applications of SiC are in space shuttles, rocket nozzles and different types of heat shields. Professor Schnack described how these materials can be fabricated and a new technique called “Thermal Gradient Method”, a process of infiltration on a substrate from a cold to a hot surface as a form of transport through diffusion. This process can be modelled as a moving boundary value problem. Mathematical simulation of this is difficult as it not only involves the description of the spatial and temporal evolution of the substrate surface, but also moving boundary descriptions. This includes discontinuities of the state variables and difficulties explicitly tracking the interface.
Professor Schnack’s research group has been able to model this process, considering gas and solid phases separated with a diffusive interface. He applies Ginzburg-Landau’s equation for the evaluation of the phase field. The computation involved also considers the mechanism of the chemical reactions.
The solution to these problems was achieved using FEM, and the results demonstrated how the concentration of SiC increases and the whole domain changes to solid state with time.
The research continues, trying to improve the numerical stability of the codes used for composites. This may be achieved by using mixed discontinuous Galerkin method, following developments with Navier Stokes equations. This will, Professor Schnack believes, produce a better FEM solution for the temporal and spatial distribution of the phase-field and concentration of the species.
The lecture was followed with great interest by the audience and generated a lively discussion. Professor Schnack received several suggestions and comments from the audience.
Wessex Institute