Numerical Analysis: Computer Science

Numerical analysis is an area of mathematics that also involves computer science to create, evaluate and implement algorithms to solve mathematical problems of a continuous nature. These mathematical problems usually originate from real-world applications of calculus, algebra, and geometry and they frequently involve variables that continuously vary, these problems usually occur in social sciences, natural sciences, medicine, business, and engineering. In the last century, the availability and growth of computers has resulted in the increased used of realistic mathematical and computational models in engineering and science. Numerical analysis has also benefited with increased sophistication, which has been used in increasingly sophisticated

It mainly deals with applying the most powerful computational machines, numerical analysis, graphical user interfaces and symbolic mathematical computation to simplify setting up, solving and interpretation of complex mathematical models that are typical of real world applications. Numerical simulations have as a result become critical assets to real world studies especially those involving fluid flow such as wind energy and wind turbines. These simulations tools have allowed for the creation of new designs and increased levels of efficiency, which were not possible before. Currently, research is being carried out to improve the efficiency of these simulation tools further. Before conduction any research into the wind and related technologies it is important to understand the functions of some numerical tools. Such information can be found in relevant journals and product websites to explore how simulation tools like ANSYS Fluent and Qblade

BY using this technique the domains of the model are discretized to a finite number of cells of control volumes. After the creation of the sets, general conservation equations for momentum, mass, energy species and many others are applied and solved within the set of controlled volumes. Also, partial differential equalities are discretized into systems of algebraic functions after which all the algebraic functions are solved numerically to create the solution field. Pre-processing, solving and post-processing guides the entire solution development process. In the preprocessing stage, the problem is identified, and the modeling goals are defined and the domain to be modeled is identified, after which the grid is designed and created. After pre-processing the solver is executed. The physical models relating to the wind turbine such as turbulence, multiphase, moving mesh and zones are created. These physical models are combined with boundary conditions, material properties, and boundary conditions in the transport equations of mass, phase volume friction, energy, momentum state equation and other supporting physical models. The solver is the executed to calculate and monitor the solution. After creating the solution, the post processing step is executed. During post-processing, the results of the simulation are evaluated, and any revisions to the model are carried out to improve the model and