The purpose of this paper is to gain some insight into the characteristic
behavior of a general compressible two-fluid gas-liquid model in 2D by using numerical
computations. Main focus is on mass transport phenomena. Relatively few
numerical results in higher dimensions can be found in the literature for this two-
fluid model, in particular, for cases where mass transport dynamics are essential.
We focus on natural extensions to 2D of known 1D benchmark test cases, like water
faucet and gas-liquid separation, previously employed by many researchers for the
purpose of testing various numerical schemes. For the numerical investigations,
the WIMF discretization method introduced in [SIAM J. Sci. Comput. 26 (2005),
1449] is applied, in combination with a standard dimensional splitting approach.
Highly complicated flow patterns are observed reflecting the balance between acceleration
forces, gravity, interfacial forces, and pressure gradients. An essential
ingredient in these results is the appearance of single-phase regions in combination
with mixture regions (dispersed flow). Solutions are calculated and shown from
early times until a steady state is reached. Grid refinement studies are included to
demonstrate that the obtained solutions are not grid-sensitive.