Date of Graduation
Eberly College of Arts and Sciences
A pseudospectral approach is used to solve non-smooth evolutionary problems using Fourier collocation and Chebyshev collocation. It is well known that pseudospectral methods for smooth problems can offer superior accuracy over finite difference and finite element methods.;This paper explores the use of pseudospectral methods for non-smooth evolutionary problems in the area of hyperbolic heat transfer. Boundary and initial conditions are considered which cause instantaneous jumps, in the temperature and flux, prior to the propagation of a thermal wave into the medium. There is a considerable amount of literature that has investigated hyperbolic heat transfer under similar conditions, the common problems throughout theses investigations is the presence of numerical oscillation at the wave front. Finite difference and finite element methods have both been used, and both methods exhibit severe numerical oscillation at the wave front. In an attempt to reduce this oscillation extremely fine grids and severe timestep restrictions had to be introduced, but even these attempts still exhibited some oscillation.;This paper will demonstrate that pseudospectral methods, when used correctly, can eliminate the numerical oscillation at the wave front and accurately resolve the instantaneous jump at the boundary. Furthermore, pseudospectral methods can be used successfully with coarser grids and larger timesteps and still provide superior results.;This paper will also investigate hyperbolic heat transfer with boundary conditions that contain a continuous periodic flux with surface radiation. These boundary conditions have never before been investigated in the literature on hyperbolic heat transfer. Previous research has only considered boundary conditions that contain a constant flux with radiation r a periodic on-off pulse with radiation. In either case, extremely fine grids were needed to prevent severe numerical oscillation. This paper will compare the hyperbolic and parabolic thermal response due to the periodic flux, under a wide range of frequencies, as well as show how pseudospectral methods can be used successfully in the case of periodic flux with surface radiation without the need to introduce fine spatial grids and prohibitively small timesteps.
Guenther, Chris Palmer, "Pseudospectral techniques for non -smooth evolutionary problems" (1998). Graduate Theses, Dissertations, and Problem Reports. 946.