Abstract
Some of the basic computational techniques are examined in this chapter to solve the governing equations of fluid dynamics. In the first stage, the computational solution involves the conversion of the governing equations into a system of algebraic equations. This is usually known as the discretization stage. Discretization tools such as the finite-difference and finite-volume methods, which are abound in many CFD applications, are described. In the second stage, the numerical solution to the system of algebraic equations can be achieved by either the use of direct or iterative methods. Gaussian elimination and the Thomas algorithm whilst point-by-point Jacobi and Gauss-Seidel methods have been described for the former and latter, respectively. Nevertheless, CFD problems are generally multidimensional and composed of a large system of equations to be solved. Efficient iterative methods such as the ADI or Stone's SIP are briefly described to solve such a system of equations. To further enhance the convergence of the computational solution, precondition conjugate gradient or multigrid methods, which accelerate the iteration process, are also discussed.
Published Version
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