  We present a pedagogical review of some of the methods employed in Eulerian
computational fluid dynamics (CFD). Fluid mechanics is governed by the Euler
equations, which are conservation laws for mass, momentum, and energy. The
standard approach to Eulerian CFD is to divide space into finite volumes or
cells and store the cell-averaged values of conserved hydro quantities. The
integral Euler equations are then solved by computing the flux of the mass,
momentum, and energy across cell boundaries. We review both first-order and
second-order flux assignment schemes. All linear schemes are either dispersive
or diffusive. The nonlinear, second-order accurate total variation diminishing
(TVD) approach provides high resolution capturing of shocks and prevents
unphysical oscillations. We review the relaxing TVD scheme, a simple and robust
method to solve systems of conservation laws like the Euler equations.
  A 3-D relaxing TVD code is applied to the Sedov-Taylor blast wave test. The
propagation of the blast wave is accurately captured and the shock front is
sharply resolved. We apply a 3-D self-gravitating hydro code to simulating the
formation of blue straggler stars through stellar mergers and present some
numerical results. A sample 3-D relaxing TVD code is provided in the appendix.
