This paper presents a new algorithm for the numerical solution of the Navier-Stokes equations coupled with the convection-diffusion equation. After establishing convergence of the semidiscrete formulation at each time step, we introduce a new iterative scheme based on a projection method called the coupled prediction scheme. We show that even though the predicted temperature is advected by a velocity prediction which is not necessarily divergence free, the theoretical time accuracy of the global scheme is conserved. From a numerical point of view, this new approach gives a faster and more efficient algorithm compared to the usual fixed-point approaches. Introduction.Heat transfer is an important factor in many fluid dynamics applications. Whenever there is a temperature difference between the fluid and the confining area, heat will be transferred and the flow will be affected in nontrivial ways. Natural convection is such an example in which the driving forces are density variations and gravity (see Jiji [28], for instance). Natural convection flows are observed in different situations such as geophysics, weather, ocean movement and are also exploited in numerous applications such as double-glazed windows, cooling in electronic devices, building insulation, etc.The model is generally described using the Boussinesq approximation. In this approximation, the density of the fluid is assumed to be constant and the gravitational source force (the buoyancy term in the momentum equation) depends on the temperature (Martynenko and Khramtsov [34]).Typically, in the Boussinesq approximation, the coupling between the fluid and the temperature appears through two terms: a source term depending linearly on the temperature, and a convective term based on the velocity of the fluid (see system (2.1)). In this paper we propose a reinforcement of this coupling by adding an explicit dependency to the temperature for the viscosity and the diffusion coefficients. Moreover, since the assumptions on the source term for the momentum equation are not essential (Remark 2.1), we will consider a more general source term. Owing to this departure from the usual Boussinesq equations, the proposed model can be viewed more generally as a thermally coupled Navier-Stokes problem.Thermally coupled incompressible flow problems present two major difficulties requiring special attention: solving the incompressible Navier-Stokes equations on very fine three-dimensional meshes in a reasonable computational time is a difficult task; the strong coupling between the Navier-Stokes and convection-diffusion equations often leads to very complex time dependent dynamics requiring efficient solvers.

-There are number of sources for generation of power but in the recent years wind energy shown its potential as the clean source of energy and contributing to the high-energy demands of the world. Vertical axis wind turbine (VAWT) is the best option for the area, which are under load sheading. Thus, in this paper, VAWT blades for low average wind speed regions like Al Khobar in Saudi arabia is designed and implemented. Performance and power produced are investigated and utilized in the design and the economic analysis. An experimental and theoretical review on the performance of Savonius VAWT is presented. The turbine was made of Aluminium alloy with a blade angle of 160 degree and maximum coefficient of power, Cp, of 0.286. The results of this current study showed that the power output, with speed of minimum speed of 12-15 m/s generate 40-80 watts with an efficiency of 31~35%.

SUMMARYIn this paper, we present an immersed boundary method for solving fluid flow problems in the presence of static and moving rigid objects. A FEM is used starting from a base mesh that does not represent exactly rigid objects (non‒body‒conforming mesh). At each time step, the base mesh is locally modified to provide a new mesh fitting the boundary of the rigid objects. The mesh is also locally improved using edge swapping to enhance the quality of the elements. The Navier–Stokes equations are then solved on this new mesh. The velocity of moving objects is imposed through standard Dirichlet boundary conditions. We consider a number of test problems and compare the numerical solutions with those obtained on classical body‒fitted meshes whenever possible. Copyright © 2014 John Wiley & Sons, Ltd.

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