creator Miksis, Zachary M. advisor Li, Xiaofan Nek5000 is a highly scalable spectral element code used in a broad array of problems in computational fluid dynamics. In this thesis, we focus on applying the code to a model problem of an accelerating Couette flow, or a hydrodynamic flow between two plates, of which the top plate is accelerating and the bottom plate is stationary, and verifying the numerical methods as applied to this problem. We obtain an analytical solution to the hydrodynamic flow problem, and use this to analyze the effects of changing time step length, the size of the computational mesh, and the computational polynomial order on the accuracy and stability of Nek5000. Additionally, we discuss the addition of an applied magnetic field to the hydrodynamic Couette flow, and provide a formulation for an exact solution to this magnetohydrodynamic problem that can be used to further verify Nek5000 in a similar fashion to the hydrodynamic problem. Submitted by Erma Thomas (thomase@iit.edu) on 2017-11-02T22:46:07Z No. of bitstreams: 1 etdadmin_upload_497371.zip: 666282 bytes, checksum: 6bd1fe2679c51c10b8b245d42bbed676 (MD5) Made available in DSpace on 2017-11-02T22:46:07Z (GMT). No. of bitstreams: 1 etdadmin_upload_497371.zip: 666282 bytes, checksum: 6bd1fe2679c51c10b8b245d42bbed676 (MD5) Previous issue date: 2017-05 M.S. In Applied Mathematics, May 2017 2017 2017-05 en computational fluid dynamics Couette flow magnetohydrodynamics Nek5000 spectral element method verification Thesis born digital application/pdf In Copyright http://rightsstatements.org/page/InC/1.0/ Restricted Access MATH / Applied Mathematics Illinois Institute of Technology Affiliated department http://hdl.handle.net/10560/islandora:7425