Wrap up and future directions: group

Group discussion of recommendations and priorities for future research.Non UBCUnreviewedAuthor affiliation: McMaster UniversityFacult

A dynamically adaptive wavelet method for the shallow water equations on the sphere: towards heterogeneous multi-scale climate models.

This talk presents a dynamically adaptive wavelet method for the shallow water equations on the staggered hexagonal C-grid on the sphere. The adaptive grid hierarchy is a dyadic subdivision of the icosahedron, which is optimized to ensure good geometric properties. Distinct biorthogonal second generation wavelet transforms are developed for the pressure and the velocity, together with compatible restriction operators to ensures discrete mass conservation and no numerical generation of vorticity. Coastlines are introduced by a new volume penalization method of the shallow water equations which ensure inertia-gravity waves are reflected physically, and that no-slip boundary conditions are imposed for the horizontal velocity. The code is fully parallelized using mpi, and we demonstrate good weak parallel scaling to at least 1000 processors. The efficiency and accuracy of the method are verified by applying it to a tsunami-type inertia-gravity wave with full topography, to wind-driven gyre flow and to homogeneous rotating turbulence. Even in the unfavourable case of homogeneous turbulence significant savings in the number of degrees of freedom are achieved by the adaptivity. This project is an initial step towards developing a full dynamically adaptive climate model. I will also discuss some outstanding issues in sub-grid parameterization of multiphysics processes (e.g. unresolved turbulence, cloud formation, precipitation, effect of topography).Non UBCUnreviewedAuthor affiliation: McMaster UniversityFacult

Group discussion of recommendations and priorities for future research.

Group discussion of recommendations and priorities for future research.Non UBCUnreviewedAuthor affiliation: McMaster UniversityFacult

Aeroservoelastic optimisation of an aerofoil with active compliant flap via reparametrisation and variable selection

To aid in the investigation of new simultaneous optimisation strategies for exible vehicles and their control systems, a two-dimensional aerofoil optimisation which demands minimal computational effort is studied. The aeroservoelastic system consists of a two-dimensional, potential flow over a deforming aerofoil; an actively controlled, but saturated compliant trailing edge; a dynamic observer that uses a series of pressure sensors on the aerofoil; and a heave/pitch linear spring model. Although computationally simple, the design allows for optimisation over multiple disciplines: the structure can be designed by varying the stiffness of the springs; the control architecture through weightings in a LQR controller; the observer by means of the placement of pressure sensors; and the aerodynamics via the shaping of the compliant trailing edge. Optimising the weight and a metric of performance over all these fields simultaneously is compared to a sequential methodology of optimising the open-loop characteristics first and subsequently adding a closed-loop con-troller. Parametrisation of the design vector and variable selection often require user input and are fixed during optimisation. Our research aims to automate this process. Further-more, we investigate whether varying the parametrisation and number of design variables during the optimisation can lead to improvements in the final design. To accomplish this, a new basis for the design vector is created via Proper Orthogonal Decomposition (POD) using the trajectories of initial optimisation paths as a “training set". This parametrisation is shown to make the optimisation more robust with respect to the initial design, and facilitate an automated variable selection methodology. This variable selection allows for the dimension of the problem to be reduced temporarily and it is shown that this makes the optimisation more robust