Type of Document Dissertation Author Call, Jay Michael Author's Email Address jcall1@tigers.lsu.edu URN etd-07052010-224427 Title Generalized Curvilinear Advection Formalism for Finite Volume Codes Doing Relativistic Hydrodynamics Degree Doctor of Philosophy (Ph.D.) Department Physics & Astronomy Advisory Committee

Advisor Name Title Tohline, Joel E. Committee Chair Frank, Juhan Committee Member Hynes, Robert Committee Member Lehner, Luis Committee Member Okeil, Ayman Dean's Representative Keywords

- matched filtering
- PPM
- piecewise parabolic method
- flux reconstruction
- AMR
- adaptive mesh refinement
- frame of reference
- Coriolis force
- centrifugal force
- inertial force
- symmetry
- physics mining
- LIGO
- simulation
- numerical model
- metric
- timestep
- time update
- Runge-Kutta
- generalized advection variable
- state variable
- grid geometry
- toy model
- Flower code
- primitive variable
- generalized Valencia formulation
- continuity equation
- momentum equation
- energy equation
- hybrid
- physical source
- standard source
- Euler equation
- TOV star
- control volume
- 3-velocity
- 4-velocity
- normal
- orthogonal
- gravitational waves
- ADM
- source
- weighted linear combination
- field equation
- characteristic vector
- flow-complementing vector
- vanishing vector
- quasi-Killing vector
- Killing vector
- coordinate basis vector
- pressure gradient
- naked pressure term
- generalized conservative variable
- flux
- conservative
Date of Defense 2010-03-29 Availability unrestricted AbstractWhile it is possible to numerically evolve the relativistic fluid equations using any chosen coordinate mesh, typically there are distinct computational advantages associated with different types of candidate grids. For example, astrophysical flows that are governed by rotation tend to give rise to advection variables that are naturally conserved when a cylindrical mesh is used. On the other hand, Cartesian-like coordinates afford a more straightforward implementation of adaptive mesh refinement (AMR) and avoid the appearance of coordinate singularities. Here it is shown that it should be possible to reap the benefits associated with multiple types of coordinate systems simultaneously in numerical simulations. This could be accomplished by implementing a hybrid numerical scheme: one that evolves a set of state variables adapted to one particular set of coordinates on a mesh defined by an alternative type of coordinate system. A formalism (a generalization of the much-used Valencia formulation) that will aid in the implementation of such a hybrid scheme is provided. It is further suggested that a preferred approach to modeling astrophysical flows that are dominated by rotation may involve the evolution of inertial-frame cylindrical momenta (i.e., radial momentum, angular momentum, and vertical momentum) and the Jacobi energy—all on a corotating Cartesian coordinate grid.

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