Development of fast deterministic solvers for the Boltzmann equation

Gas flows in hyper-sonic air breathing engines and rocket thrusters and flows of particles into vacuum contain regions where the distribution of particle velocities deviates significantly from the Maxwellian distribution. The gas in these regions is said to be in the non-continuum state and its evolution is best described using kinetic equations. The most physically accurate model of non-continuum gas is given by the Boltzmann kinetic equation. However, because of the very high computational costs associated with the evaluation of the collision integral, solution of the Boltzmann equation is used sparingly. Simpler approximate models are often desired in simulations of non-continuum flows in multidimensional applications. However, validating simpler models may be not easy when experimental data is not available. The goal of thesis is to develop novel capabilities for high-fidelity simulation of non-continuum flows with guaranteed accuracy. We will address the our goal by developing fast solvers for the Boltzmann equation using sparse Galerkin approximations of the velocity distribution function and by evaluating accuracy of these solvers using parallel fully deterministic discontinuous Galerkin (DG) Boltzmann solver.