The goal of this research is to develop accurate and efficient computational algorithms that will enable engineers to routinely analyze transport phenomena without relying on methods that utilize simplified physical models. In particular, several methods to accelerate the interactive convergence of numerical transport solutions will be examined, they include: developing the diffusion synthetic acceleration algorithm (DSA) in multidimensional geometries, applying a multigrid method for the acceleration on inner iterations, and applying a "synthetic" acceleration method for the acceleration of outer iterations. Transport process is characterized by the movement of some quantity in an interacting medium. The transport of heat in a solid, of steam-water mixture in a heat exchanger, or of photons in the upper atmosphere, are all examples of transport process. Transport process can be categorized as continuum or particle depending on whether one describe the transfer of continuum quantities; e.g. mass, momentum, or energy, or particles; e.g. protons or neutrons. However, if the number density of the particles are sufficiently large, then the detailed statistical fluctuations can be smeared out so that an approximate continuum formulation may be used; i.e. Boltzman transport equation which for the linear case can be further reduced to a diffusion limit. The key issue is to strike a balance between the accuracy and efficiency (cost) of doing the computations associated with each of these formulations
