Rhomax is the total density of the mixture. This is a hydrostatic flow
with the gravity force being in the top to bottom direction. If the
initial profiles were the exact solutions the calculation would not change
at the numerical solution advances in time. However for this calculation, the initial
profiles were taken as constant density and pressure with the velocities set to
zero. Thus the initial potential energy is greater than the steady-state energy
so the computed solutions develop an oscillatory motion about the steady
state. As the Euler equations are being solved, there is no physical
dissipation to eliminate the excess energy in the initial profiles
(only a small dissipation introduced by the numerical scheme)
and therefore the computed solutions remains oscillatory in time. The third-order
time difference scheme of Shu was used. The spatial scheme is second-order
accurate. The object of this comparison is to show that the solutions between
the 2D and 3D codes agree.
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