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.
| Identifer | oai:union.ndltd.org:LSU/oai:etd.lsu.edu:etd-04022014-210318 |
| Date | 16 April 2014 |
| Creators | Byerly, Zachary Duncan |
| Contributors | Tohline, Joel, Frank, Juhan, Hynes, Robert, Lee, Hwang, Adkins, William |
| Publisher | LSU |
| Source Sets | Louisiana State University |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lsu.edu/docs/available/etd-04022014-210318/ |
| Rights | unrestricted, I hereby certify that, if appropriate, I have obtained and attached herein a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to LSU or its agents the non-exclusive license to archive and make accessible, under the conditions specified below and in appropriate University policies, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. |
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