Development of higher order numerical procedures for the solution of fluid flow and heat transfer equations

The objective of this thesis is to develop and analyze two higher order numerical schemes for the solution of fluid flow and heat transfer equations. These schemes are derived on the same theme as the well known exponential differencing scheme. The exponential differencing scheme is based on the locally one-dimensional profile assumption that the total flux (i.e. conduction and diffusion) is constant between grid points. Therefore, if the problem is one-dimensional and the source term in the convection-diffusion equation is equal to zero, the exponential scheme will produce the exact solution. However, most practical problems are multidimensional and involve significant source terms. For such problems, the exponential scheme is generally not very accurate. The first scheme that is developed in this thesis, called LOAD0, is derived on the assumption that the total flux has a linear variation between grid points. The second new scheme, called LOAD1, is derived on the assumption that the total flux has a quadratic variation between grid points.