Analytical method numerical simulation software

The key methods that are the focus of this section are categorized as analytical versus numerical methods. Analytical methods can be solved using explicit equations. In some cases, the methods can be conveniently applied using pencil and paper, although for most practical problems, such methods are more commonly coded into a spreadsheet or other software. Analytical methods can provide exact solutions for some specific situations. Unfortunately, such situations are not often encountered in practice. Numerical methods require the use of a computer simulation package. They offer the advantage of broader applicability and flexibility to deal with a wide range of input distribution types and model functional forms and can produce a wide variety of output data. 

The IDA generator-collector system has been simulated using the Laasonen (BI) scheme [374], explicit FD [375, 376], hopscotch and conformal mapping [220], the finite analytic numerical method [152], extrapolation using expanding space intervals [332] and ADI with expanding space intervals [348, 377]. Commercial FEM software packages Flux-Expert [324] and COMSOL Multiphysics [378] have also been employed. 

To analyze the airflow pattern, simulation of airflow was carried out using a fluid flow analysis package. Fluent 6.1 [1,6-12]. To solve the three-dimensional airflow field inside the nozzles, a CFD model was developed using the above software. Fluid flow and related phenomena can be described by partial differentiation equations, which caimot be solved analytically except in over-simplified cases. To obtain an approximate solution numerically, a discretization method to approximate the differential equations by a system of algebraic equations, which can be then numerically solved on a computer. The approximations were applied to small domains in space and/or time so the numerical solution provides results at discrete locations in space and time. Much of the accuracy depends on the quality of the methodology used, for which CFD is a powerful tool to predict the flow behavior of fluid inside any object. It provides various parameters such as air velocity profiles (axial, tangential, resultant etc.) and path lines trajectory, which are important for subsequent analysis. It was for those reasons that a CFD package. Fluent 6.1, which uses a Finite Volume (FV) method, was employed for airflow simulation. 

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