** Objective **

1. Explore various numerical strategies to achieve a fast and also accurate computation
for low Mach multiphase flows

2. Well-balanced treatment for gravitational source terms

** Problem description **

with a rectangular column of water of size a=0.06m width and h=0.12m high. The computational domain
is a rectangular region of 0.5m width and 0.15m high. All the boundaries are treated as solid walls
numerically. Under the gravity where we have g= 9.8 m/s^2, the water column collapses.
Note that there exist many mathematical models to describe the physical feature of this problem;
see a sample of them in below. No matter what mathematical model and numerical method are used
in practice, your numerical results should be in comparison with the experimental data on the time
history of

** Mathematical model **

** Sample computations **

** Related references **

1. J. C. Martin and W. J. Moyce, Part IV. An experimental study of the collapse of liquid columns on a rigid horizontal plane , Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 244, No. 882 (Mar. 4, 1952), pp. 312-324

2. J. C. Martin and W. J. Moyce, Part V. An Experimental Study of the Collapse of Fluid Columns on a Rigid Horizontal Plane, in a Medium of Lower, but Comparable, Density , Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 244, No. 882 (Mar. 4, 1952), pp. 325-334

3. M. A. Cruchaga, D. J. Celentano, and T. E. Tezduyar, Collapse of a liquid column: numerical simulation and experimental validation , Comput. Mech. (2007) 39: 453¡V476

4. A. Murrone and H. Guillard, A five reduced equation model for compressible two-phase flow problems , J. Comput. Phys. (2004) 202: 664-698

5. A. Murrone and H. Guillard, Behavior of upwind scheme in the low Mach number limit: III. Preconditioned dissipation for a five equation two phase model , Computers and Fluids (2008) 37: 1209-1224

6. K.-M. Shyue, An efficient shock-capturing algorithm for compressible multicomponent problems , J. Comput. Phys. (1998) 142: 208-242