Application and analysis of sinc numerical methods to heat and fluid flow problems.

摘要

Numerical methods have played an important role in the solution of engineering problems where an analytical solution is impossible or hard to obtain. Some of the numerical methods that have been used in the past and still in use include the finite difference method, finite element method and boundary element method. A new addition to this challenging area of numerical methods is the sine numerical method. Sinc numerical method excels over other numerical methods with respect to handling problems with singularities and semi-infinite domains. They provide a more efficient way of setting up the algebraic equations corresponding to the governing differential or integral equations.; In this dissertation, the sinc numerical method was applied to some heat conduction and fluid flow problems and compared against other numerical methods for accuracy and computational time. In the case of the heat conduction problems, a newly formulated sinc harmonic method was applied for the solution of the Laplace equation. The two heat conduction problems that were solved using the sinc harmonic method were heat conduction in a square and in a semi-infinite medium. The ability of the sinc method to handle singularities and semi-infinite domains were clearly demonstrated in these two heat conduction problems. In the case of the two-dimensional Navier Stokes equations, sinc collocation was used for the solution of the driven cavity and the flat plate problem. The pressure correction approach was applied for the solution of the two-dimensional Navier Stokes equations using the sinc collocation method. The pressure correction approach employed in this study in the solution of the Navier Stokes equations involved calculation of the velocity derivatives at the boundary. Due to the drawback of the sinc numerical method in handling this situation, finite difference method was used to calculate the pressure correction on the boundary. The study also shows a comparison of the results obtained from the sinc collocation method with the finite difference method and other commercial fluid dynamics code (FLUENT). This thesis is a first step in applying sinc collocation to non-linear Navier Stokes equations and some typical fluid dynamics problems.