Degree Type
Thesis
Date of Award
2019
Degree Name
Master of Science
Department
Mathematics
Major
Applied Mathematics
First Advisor
James . Rossmanith
Abstract
This paper provides a high-order numerical scheme for solving thin-film models of the
form q_t + (q^2 - q^3)_x = -(q^3 q_{xxx})_x.
The second term in this equation is of nonlinear hyperbolic type, while the right-hand
side is of nonlinear parabolic type.
The nonlinear hyperbolic term is discretized with the standard modal discontinuous
Galerkin method, and the nonlinear parabolic term is discretized with the local
discontinuous Galerkin method.
Propagation in time is done with an implicit-explicit Runge-Kutta scheme so as to
allow for larger time steps.
The timestep restriction for these methods is determined by the hyperbolic wavespeed
restriction, and is not limited by the nonlinear parabolic term.
A novel aspect of this method is that the resulting nonlinear algebraic equations
are solved with a Newton-free iteration with a Picard iteration.
The number of iterations required to converge is less than or equal to the estimated
order of the method.
We have demonstrated with this method up to third order convergence.
Copyright Owner
Caleb Logemann
Copyright Date
2019-12
Language
en
File Format
application/pdf
File Size
48 pages
Recommended Citation
Logemann, Caleb, "An implicit-explicit discontinuous Galerkin scheme using a newton-free Picard iteration for a thin-film model" (2019). Graduate Theses and Dissertations. 17734.
https://lib.dr.iastate.edu/etd/17734
