Active flow control bump design using hybrid Nash-game coupled to evolutionary algorithms

In this paper, the optimal design of an active flow control device; Shock Control Bump (SCB) on suction and pressure sides of transonic aerofoil to reduce transonic total drag is investigated. Two optimisation test cases are conducted using different advanced Evolutionary Algorithms (EAs); the first optimiser is the Hierarchical Asynchronous Parallel Evolutionary Algorithm (HAPMOEA) based on canonical Evolutionary Strategies (ES). The second optimiser is the HAPMOEA is hybridised with one of well-known Game Strategies; Nash-Game. Numerical results show that SCB significantly reduces the drag by 30% when compared to the baseline design. In addition, the use of a Nash-Game strategy as a pre-conditioner of global control saves computational cost up to 90% when compared to the first optimiser HAPMOEA.

The importance of a triple bottom line approach for safeguarding urban water quality

Water environments are greatly valued in urban areas as ecological and aesthetic assets. However, it is the water environment that is most adversely affected by urbanisation. Urban land use coupled with anthropogenic activities alters the stream flow regime and degrade water quality with urban stormwater being a significant source of pollutants. Unfortunately, urban water pollution is difficult to evaluate in terms of conventional monetary measures. True costs extend beyond immediate human or the physical boundaries of the urban area and affect the function of surrounding ecosystems. Current approaches for handling stormwater pollution and water quality issues in urban landscapes are limited as these are primarily focused on ‘end-of-pipe’ solutions. The approaches are commonly based either on, insufficient design knowledge, faulty value judgements or inadequate consideration of full life cycle costs. It is in this context that the adoption of a triple bottom line approach is advocated to safeguard urban water quality. The problem of degradation of urban water environments can only be remedied through innovative planning, water sensitive engineering design and the foresight to implement sustainable practices. Sustainable urban landscapes must be designed to match the triple bottom line needs of the community, starting with ecosystem services first such as the water cycle, then addressing the social and immediate ecosystem health needs, and finally the economic performance of the catchment. This calls for a cultural change towards urban water resources rather than the current piecemeal and single issue focus approach. This paper discusses the challenges in safeguarding urban water environments and the limitations of current approaches. It then explores the opportunities offered by integrating innovative planning practices with water engineering concepts into a single cohesive framework to protect valuable urban ecosystem assets. Finally, a series of recommendations are proposed for protecting urban water resources within the context of a triple bottom line approach.

Novel analytical and numerical methods for solving fractional dynamical systems

During the past three decades, the subject of fractional calculus (that is, calculus of integrals and derivatives of arbitrary order) has gained considerable popularity and importance, mainly due to its demonstrated applications in numerous diverse and widespread fields in science and engineering. For example, fractional calculus has been successfully applied to problems in system biology, physics, chemistry and biochemistry, hydrology, medicine, and finance. In many cases these new fractional-order models are more adequate than the previously used integer-order models, because fractional derivatives and integrals enable the description of the memory and hereditary properties inherent in various materials and processes that are governed by anomalous diffusion. Hence, there is a growing need to find the solution behaviour of these fractional differential equations. However, the analytic solutions of most fractional differential equations generally cannot be obtained. As a consequence, approximate and numerical techniques are playing an important role in identifying the solution behaviour of such fractional equations and exploring their applications. The main objective of this thesis is to develop new effective numerical methods and supporting analysis, based on the finite difference and finite element methods, for solving time, space and time-space fractional dynamical systems involving fractional derivatives in one and two spatial dimensions. A series of five published papers and one manuscript in preparation will be presented on the solution of the space fractional diffusion equation, space fractional advectiondispersion equation, time and space fractional diffusion equation, time and space fractional Fokker-Planck equation with a linear or non-linear source term, and fractional cable equation involving two time fractional derivatives, respectively. One important contribution of this thesis is the demonstration of how to choose different approximation techniques for different fractional derivatives. Special attention has been paid to the Riesz space fractional derivative, due to its important application in the field of groundwater flow, system biology and finance. We present three numerical methods to approximate the Riesz space fractional derivative, namely the L1/ L2-approximation method, the standard/shifted Gr¨unwald method, and the matrix transform method (MTM). The first two methods are based on the finite difference method, while the MTM allows discretisation in space using either the finite difference or finite element methods. Furthermore, we prove the equivalence of the Riesz fractional derivative and the fractional Laplacian operator under homogeneous Dirichlet boundary conditions – a result that had not previously been established. This result justifies the aforementioned use of the MTM to approximate the Riesz fractional derivative. After spatial discretisation, the time-space fractional partial differential equation is transformed into a system of fractional-in-time differential equations. We then investigate numerical methods to handle time fractional derivatives, be they Caputo type or Riemann-Liouville type. This leads to new methods utilising either finite difference strategies or the Laplace transform method for advancing the solution in time. The stability and convergence of our proposed numerical methods are also investigated. Numerical experiments are carried out in support of our theoretical analysis. We also emphasise that the numerical methods we develop are applicable for many other types of fractional partial differential equations.