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Relativistic Viscous Hydrodynamics for High Energy Heavy Ion Collisions

It has been over a decade since the first experimental data from gold nuclei collisions at the Relativistic Heavy Ion Collider suggested hydrodynamic behavior. While early ideal hydrodynamical models were surprisingly accurate in their predictions, they ignored that the large longitudinal velocity gradient meant that even small shear viscosity would produce large corrections to the transverse dynamics. In addition, much less was known about the equation of state predicted by lattice calculations of quantum chromodynamics, which predicts a soft region as the degrees of freedom change from quarks to hadrons but no first-order phase transition. Furthermore, the effects of late, dilute stage rescattering were handled within the hydrodynamic framework to temperatures where local kinetic equilibrium is difficult to justify. This dissertation presents a three-dimensional viscous hydrodynamics code with a realistic equation of state coupled consistently to a hadron resonance gas calculation. The code presented here is capable of making significant comparisons to experimental data as part of an effort to learn about the structure of experimental constraints on the microscopic interactions of dense, hot quark matter.