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Abstract: In this paper we apply the recently developed mimetic discretization method to the mixed formulation of the Stokes problem in terms of vorticity, velocity and pressure. The mimetic discretization presented in this paper and in Kreeft et al. [51] is a higher-order method for curvilinear quadrilaterals and hexahedrals. Fundamental is the underlying structure of oriented geometric objects, the relation between these objects through the boundary operator and how this defines the exterior derivative, representing the grad, curl and div, through the generalized Stokes theorem. The mimetic method presented here uses the language of differential k-forms with k-cochains as their discrete counterpart, and the relations between them in terms of the mimetic operators: reduction, reconstruction and projection. The reconstruction consists of the recently developed mimetic spectral interpolation functions. The most important result of the mimetic framework is the commutation between differentiation at the continuous level with that on the finite dimensional and discrete level. As a result operators like gradient, curl and divergence are discretized exactly. For Stokes flow, this implies a pointwise divergence-free solution. This is confirmed using a set of test cases on both Cartesian and curvilinear meshes. It will be shown that the method converges optimally for all admissible boundary conditions. [Copyright &y& Elsevier]

Abstract: A new formulation of Kapila’s five-equation model for inviscid, non-heat-conducting, compressible two-fluid flow is derived, together with an appropriate numerical method. The new formulation uses flow equations based on conservation laws and exchange laws only. The two fluids exchange momentum and energy, for which exchange terms are derived from physical laws. All equations are written as a single system of equations in integral form. No equation is used to describe the topology of the two-fluid flow. Relations for the Riemann invariants of the governing equations are derived, and used in the construction of an Osher-type approximate Riemann solver. A consistent finite-volume discretization of the exchange terms is proposed. The exchange terms have distinct contributions in the cell interior and at the cell faces. For the exchange-term evaluation at the cell faces, the same Riemann solver as used for the flux evaluation is exploited. Numerical results are presented for two-fluid shock-tube and shock-bubble-interaction problems, the former also for a two-fluid mixture case. All results show good resemblance with reference results. [Copyright &y& Elsevier]

Global warming has focused attention on how the world produces the energy required to power the planet. It has driven a major need to move away from using fossil fuels for energy production toward cleaner and more sustainable methods of producing renewable energy. The development of offshore windfarms, which harness the power of the wind, is seen as a viable approach to creating renewable energy but they can be difficult to design efficiently. The complexity of their design can benefit significantly from the use of computational optimisation. The windfarm optimisation problem typically consists of two smaller optimisation problems: turbine placement and cable routing, which are generally solved separately. This paper aims to utilise selection hyper-heuristics to optimise both turbine placement and cable routing simultaneously within one optimisation problem. This paper identifies and confirms the feasibility of using selection hyper-heuristics within windfarm optimisation to consider both cabling and turbine positioning within the same single optimisation problem. Key results could not identify a conclusive advantage to combining this into one optimisation problem as opposed to considering both as two sequential optimisation problems. [ABSTRACT FROM AUTHOR]