Identifier
etd-04022014-210318
Degree
Doctor of Philosophy (PhD)
Department
Physics and Astronomy
Document Type
Dissertation
Abstract
We demonstrate the capabilities of a new hybrid scheme for simulating dynamical fluid flows in which cylindrical components of the momentum are advected across a rotating Cartesian coordinate mesh. This hybrid scheme allows us to conserve angular momentum to machine precision while capitalizing on the advantages offered by a Cartesian mesh, such as mesh refinement. The work presented here focuses on measuring the real and imaginary parts of the eigenfrequency of unstable axisymmetric modes that naturally arise in massless polytropic tori having a range of different aspect ratios, and quantifying the uncertainty in these measurements. Our measured eigenfrequencies show good agreement with the results obtained from the linear stability analysis of Kojima (1986) and from nonlinear hydrody- namic simulations performed on a cylindrical coordinate mesh by Woodward et al. (1994). When compared against results conducted with a traditional Cartesian advection scheme, the hybrid scheme achieves qualitative convergence at the same or, in some cases, much lower grid resolutions and conserves angular momentum to a much higher degree of precision. As a result, this hybrid scheme is much better suited for simulating astrophysical fluid flows, such as accretion disks and mass-transferring binary systems.
Date
2014
Document Availability at the Time of Submission
Release the entire work immediately for access worldwide.
Recommended Citation
Byerly, Zachary Duncan, "A hybrid advection scheme for conserving angular momentum on a refined Cartesian mesh" (2014). LSU Doctoral Dissertations. 1548.
https://repository.lsu.edu/gradschool_dissertations/1548
Committee Chair
Tohline, Joel
DOI
10.31390/gradschool_dissertations.1548