| dc.description.abstract | The capability to simulate moving and rotating features such as fans, turbines and stirrers is essential in many fluid dynamics applications, with wide-reaching applications ranging from wind turbine design to food science. Such simulations are inherently unsteady in time, and the increasing capability of modern computing hard- ware means that high-fidelity simulations can give detailed insight into their physics. This is achieved through novel high-order simulations, such as the discontinuous Galerkin (DG) method, which are presently popular in the setting of high-fidelity simulations.
In this thesis, we investigate the implementation of sliding interfaces within the Nektar++ spectral/hp element framework. In this setting, a region of a domain is allowed to slide via a translation or rotation. This is a simple yet powerful tool in the simulation of moving meshes since, for example, a fan can be embedded in a cylindrical region of the domain. However, at higher orders, such techniques are yet to be widely documented: particularly for complex, three-dimensional bodies. Maintaining high- order accuracy across the non-conformal interfaces that are generated in these problems is a key challenge to overcome.
We outline the general implementation of two varieties of moving meshes, using a more traditional mortar-based approach and comparing this to a more novel point-to-point method. These implementations are compared from the standpoint of numerical properties and their overall efficiency within Nektar++. To enhance performance, particularly for the point-to-point method, we investigate novel numer- ical approaches to polynomial interpolation and differentation via the barycentric formulation of Lagrange interpolants. Performance is also considered with regards to the implementation of the point-to-point method on parallel computing architectures, with modern message passing interface (MPI) implementation practices, such as neighbourhood collectives, utilised in order to further enhance performance.
Finally, we outline the arbitrary Lagrangian-Eulerian formulation for the DG method, building on the non-conformal interface handling, resulting in a working prototype of full moving mesh solver in Nektar++. We highlight results first for the linear transport equation, before moving on to the the non-linear compressible Euler and Navier-Stokes equations. These demonstrations show good results as a viable proof-of-concept for further development. | en_GB |
