Download or read book Development of Fast Deterministic Solvers for the Boltzmann Equation written by Syuzanna Aghazaryan and published by . This book was released on 2018 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: In rarefied and non-continuum conditions, gas is best described at the molecular level and the most physically accurate model is due to the Boltzmann equation. The complexity of the Boltzmann equation suggests that solutions to applications arising in engineering and physics can only be computed numerically. However, solving the Boltzmann equation is extremely difficult because of the high dimensionality of the equation and the high computational costs of evaluation of the collision integral. The objective of this thesis is to accelerate evaluation of the collision integral by replacing deterministic Gauss quadratures in the nodal-DG discretizations of the collision operator with Korobov quadratures. We developed and implemented an algorithm for computing the Boltzmann collision operator using Korobov integration. Accuracy of the multidimensional quadrature formulas was investigated on tests in idealized settings where the exact solutions are known. The method was implemented in FORTRAN. Results of evaluation of the collision operator using Korobov integration was compared to results of evaluation using full tensor product Gauss quadratures.