Cfd modelling of h-darrieus vertical axis wind turbine

CHAPTER 3: THEORY 
3.1 FINITE VOLUME METHOD- AN OVERVIEW 
In resolving the partial differential equations, the Finite Volume Method is one of the most powerful 
and widely used numerical methods. It is a numerical method where the PDE expressing 
conservation laws over the differential volumes are transformed into distinct algebraic equations 
over finite volumes (or elements or cells). Just like the finite difference method or finite element 
method, discretization of the geometric domain is the first step of this method also. Discretization 
into non-overlapping elements or finite volumes of the entire geometric domain into algebraic 
equations is done. The PDE are then transformed or discretized into algebraic equations and this is 
done by integrating them over all the distinct elements. Next, the values of the dependent variables 
at each of the elements are calculated by solving the system of algebraic equations. 
In this method, sometimes, some of the terms turns into face fluxes in the conservation equation and 
are evaluated in the faces of the finite volumes. Here, the flux entering a particular volume is equal 
to that of the flux leaving the adjacent volume. Hence, this method is conservative. So this method is 
mostly preferred in CFD due to this inherent conservation property. This method also has other 
important features. This can be applied to solve complex geometries as it can be formulated in the 
physical space on unstructured polygonal meshes. It also provides another advantage- since the 
unknown values are calculated at the cell centers or centroids of the volume elements, FVM can be 
implement a variety of boundary conditions. 
All these advantages and characteristics have made the FVM one of the most applicable numerical 
techniques to solve numerical simulations of a wide variety of applications including heat and mass 
transfer, fluid flow etc. This method’s improvement is closely entwined with CFD, and now is 
applied to solve complex geometries and applications. [56] 

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Figure 8: Finite Volume Method grid [57]