This dissertation focuses on the analysis and computation of a certain high order accurate numerical scheme which is used to solve problems in computational Cosmology. The algorithm is based on the weighted essentiallynon-oscillatory (WENO) scheme for Boltzmann-like integral differential equations. The numerical method is illustrated with applications in Astrophysics that define the transfer and scattering of photons by Hydrogen gas during the formation of the first stars in 'Early Universe'.The algorithm is designed with the aim of resolving solutions of partial differential equations with sharp fronts propagating with time. This high order accurate class of numerical technique, WENO method, is well suited for shock capturing in solving conservation laws. The numerical approximation method, in the algorithm, is coupled with high order time marching as well as integration techniques designed to reduce computational cost. This numerical algorithm is used in several applications in cosmology to help understand questions about certain physical phenomena which occurred during the formation and evolution of first generation stars.The thesis is divided broadly in terms of the algorithm and its application to thedifferent galactic processes. The first chapter deals with the astrophysical problemand offers an introduction to the numerical algorithm. In chapter 2 we outline themathematical model and the various functions and parameters associated with themodel. We also give a brief description of the relevant physical phenomena and theconservation laws associated with them.In chapter 3, we give a detailed description of the higher order algorithm and itsformulation. We also highlight the special techniques incorporated in the algorithmin order to make it more suitable for handling cases which are computationally intensive.In the later chapters, 4-7, we explore in detail the physical processes and the different applications of our numerical scheme. We calculate different results such as the time scale of a temperature coupling mechanism, radiation and intensity changes etc. Different tests are also performed to illustrate the stability and accuracy of this algorithm. Chapter 8 is concerned with ongoing work and the future research that will be carried out in this topic.
Roy, Ishani,
"High Order WENO Scheme for Computational Cosmology"
(2010).
Applied Mathematics Theses and Dissertations.
Brown Digital Repository. Brown University Library.
https://doi.org/10.7301/Z0833Q7J
