3.1 Bowshock: init_bow (Vector plot is in R-Theta coordinates)

    We have included a generic test problem of a plane parallel flow past a rigid sphere or cylinder (for ngeomx = 2 or 1, respectively).  This test problem verifies the geometry dependent terms and fictitious forces by evolving a plane parallel flow on a curvilinear grid.  The inner radial boundary conditions is reflecting (the solid sphere/ cylinder), and the outer radial boundary is set for free inflow/outflow.  The angular boundaries (theta = 0, pi) are set for reflecting conditions.  The grid is initialized with a uniform flow at Mach number umach set in init.f  The resulting simulations compare favorably with shadow-graph images of similar experiments in fluid flow.  In particular, the presence of the slip line and a shock reflecting off the axis behind the sphere agree well with supersonic flow experiments.

3.2 Colliding Blastwave: init_cbw

    A high resolution 1D test problem taken from Woodward & Colella (1984).

Do not have a Movie for this simulation

3.3 Hawley-Zabusky Shock Tube: init_hzs

    A 2d Cartesian shock tube problem described in Hawley & Zabusky (19??).  A planar shock of Mach number 1.2 impinges an oblique discontinuity separating unshocked gas with a density contrast of dratio (=3) across the discontinuity.  In order to see the long term evolution (including the roll-up of the KH instability along the contact discontinuity), imax should be made much bigger (ie, make the box long and skinny).

3.4 Kelvin_Helmholtz Instability: init_khi

    The evolution of the Kelvin-Helmholtz instability at a shear surface is simulated in a 2D cartesian box.  (Note that this could easily be done in 3D as well.)  The top and bottom of the computational domain have opposite X velocity producing a shear layer in the middle.  This contact is wiggled (a sin wave) in order to excite the KH instability.  Density of the two fluids is slightly different to make the instability visible.

3.5 Sod Shock Tube: init_sod

    The Sod shock tube has become a standard test problem in computational hydrodynamics.  The initial conditions are very simple. a contact discontinuity separating gasses with different pressures and densities.  In the standard case the density and pressure on the left are unity, and the density on the right side on the contact is 0.125 and the pressure is 0.1.  As the evolution begins, a shock propagates to the the right while a rarefaction wave travels to the left.  In the standard case these waves are relatively weak, and most hydro codes produce good results.  A more demanding test is imposed if the initial density and pressure rations are increased by an order of magnitude!
    This problem can be expanded to multiple dimensions by placing the discontinuity across a 2D or 3D grid.  We have chosen to position the contact at a 45 degree angle so that the shock and rarefaction wave propagate diagonally across the grid.

3.6 Strong, Standing Shockwave: init_sss

    A nearly stationary, shock is the Achilles heel of the PPM method.  This problem sets up a strong, standing shock in 1D (2D and 3D can also be done), allowing one to readily see the strong post shock oscillations and the effects on this numerical noise of any dissipation scheme.

Do not have a Movie for this simulation

3.7 Sedov_Taylor Blastwave: init_stb

    A Sedov-Taylor Blastwave is created on a 2D cylindrical (R-Z) grid by setting the pressure in the bottom-left 4 zones (at the origin) to some very high value.  The expansion of this high pressure region drives a spherical blastwave into the surrounding uniform medium.  The radial profile of this blastwave should match the analytic solution of a point explosion in a uniform medium given by Sedov (1959)

3.8 Stellar Wind Bubble: init_swb (Vector plot is in R-Theta coordinates)

    A supersonic wind originates at the xmin surface on a 2D spherical grid.  This wind blows a spherical bubble into the surrounding medium, sweeping up the surrounding gas into s thin shell.