Work on developing a formal structure for multiscale methods, framed in terms of wavelet methods for turbulence modelling continues under the direction of Dr Rob Prosser, in collaboration with University of Cambridge. The intention is to develop multi-resolution representations of differential operators, dyadic and triadic non-linearities. The ultimate objective is to produce families of turbulence models that generalize and extend existing two scale large eddy simulation (LES) turbulence models.
Another example of our blending of modelling approaches is the work on fluid structure interaction by Dr Prosser and Dr Keith Davey. Here, we have developed a weighted transport equation approach, which ties together the strengths of FEM and finite volume methods. The objective is to derive a family of monolithic algorithms that are able to control the energy flux through the computational domain, which is essential to maintain stability, while simultaneously allowing the easy turbulence model inclusivity of finite volume methods. The project has been the PhD project of Ms. M Ya-Alimidad and has been funded by EDF. Two proposals to EPSRC in this area are in progress: one on Fluid Structure Interaction and Blade Element Methods by Dr Prosser and Professor Dominique Laurence; and the other on Computational Solid Mechanics and Computational Fluid Dynamics for Fluid structure Interaction by Dr Prosser and Dr Davey.
The work of Dr Robert Prosser and Prof Dominique Laurence on Direct Numerical Simulation continues with the development of local boundary conditions for time dependent, Low Mach number turbulent reacting flows. The actual development of the Low Mach number conditions is essentially complete; what remains are those sets of zero measure (domain corners) where the local one dimensional approximations typically fail. Guidance on further developments is being taken from non local methods such as the difference potential methods championed by Dr Sergei Utyuzhnikov. As this area of work comes to technical maturity, we have moved towards stability studies of differential operators in the presence of heat release, exploring the link between Lyapunov stability, LHP stability and GKS stability in the presence of heat releasing structures, or flames.