Goal Adaptive Discretization of a One-Dimensional Boltzmann Equation

Goal Adaptive Discretization of a One-Dimensional Boltzmann Equation

Hoitinga, W.

De Borst, R. (promotor)
Van Brummelen, E.H. (promotor)

Aerospace Engineering

Mechanics, Aerospace Structures & Materials

2011-11-14

Fluid-flow problems in the transitional molecular/continuum regime play an important role in many engineering applications. Such problems are gaining further prominence with the perpetual trend towards miniaturization in science and engineering. The numerical simulation of flows in the transitional molecular/continuum regime and the determination of macroscale quantities from such simulation poses a fundamental challenge, on account of the complexity of the corresponding model equations. The Boltzmann equation gives a description of flow problems residing in the transitional molecular/continuum regime. The thesis entitled Goal Adaptive Discretization of a One-Dimensional Boltzmann Equation concerns the efficient discretization of a Boltzmann-type equation. We present a one-dimensional Boltzmann-type equation, which shares many important properties with its conventional counterpart. Furthermore, in a series of numerical experiments we present goal-adaptive discontinuous Galerkin finite-element approximations, which show that goal-adaptive methods are potential methods for the efficient approximation of the conventional Boltzmann equation.

Boltzmann Equation
Goal-Adaptive methods
Error Estimation
Discontinuous Galerkin
Finite Element Method

http://resolver.tudelft.nl/uuid:89c2ecfe-f5f0-4a9b-b3a5-e1d48d53860e

9789461901064

Institutional Repository

doctoral thesis

(c) 2011 Hoitinga, W.