WHY MOST TVD scheme failed in the pure convection
 

I test a pure convective flow problem. The velocity field is known as (1,1,0) . At the left boundary, T=1; at the bottom boundary T=0.
The equation is div(pUT)=0 for pure convection.

I use scalarTransportFoam to test the case. And the transport properties
is set to 0 because of no diffusion.

1 ------------
| |
| |
| |
| |
------------
0 1

I test the scheme of upwind,linear,blended 0.5,Minmod,MUSCL,SuperBee.
To my surprise, most high order schemes failed.

What the reasons? Something wrong with my case definition or code?

The attach files is the zipped case.

Any sugguestions are appreciated!

The domain is X=0 to 1 and Y =0 to 1. The mesh is 10*10.