Date of Award
Spring 2019
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
School
Mathematics and Natural Sciences
Committee Chair
James V. Lambers
Committee Chair School
Mathematics and Natural Sciences
Committee Member 2
Haiyan Tian
Committee Member 2 School
Mathematics and Natural Sciences
Committee Member 3
Zhifu Xie
Committee Member 3 School
Mathematics and Natural Sciences
Committee Member 4
Huiqing Zhu
Committee Member 4 School
Mathematics and Natural Sciences
Abstract
Existing time-stepping methods for PDEs such as Navier-Stokes equations are not as efficient or scalable as they need to be for high-resolution simulation due to stiffness. The failure of existing time-stepping methods to adapt to changes in technology presents a dilemma that is becoming even more problematic over time. By rethinking approaches to time-stepping, dramatic gains in efficiency of simulation methods can be achieved. Krylov subspace spectral (KSS) methods have proven to be effective for solving time-dependent, variable-coefficient PDEs. The objective of this research is to continue the development of KSS methods to provide numerical solution methods that are far more efficient and scalable to high resolution for Navier-Stokes equations. We will utilize these techniques for compressible Navier-Stokes equations on rectangular domains.
Copyright
2019, Brianna Bingham
Recommended Citation
Bingham, Brianna, "Scalable Time-Stepping for Navier-Stokes Through High-Frequency Analysis of Block Arnoldi Iteration" (2019). Dissertations. 1649.
https://aquila.usm.edu/dissertations/1649