Simulation of BB flow between to constant density with elliptic support using direct solve of MA + states constraints
(2nd boundary condition for MA solver) and
just interpolation later
Credit Froese Oberman (SFU) and Benamou Mokaplan
Animations show the deformation of the computational (initialy cartesian) grid under the optimal mapping.
A more complicated example with mass moving inside the domain :
This example shows how the support of the geodesic may contract from the boundary.
The grid (512 by 512) is too tight to be seen except in the dilatation zone at the end.
A new example showing the motion of a gaussian. Background density is non zero (0.2) and max of the density is 5.2.
Here we inverted the densities (background is 5.2 and minimum density 0.2)
Not much happens as there is plenty of mass everywhere. Some translation is bound to occur though ….
It can be seen on this zoom in the expansion zone, the final mesh motion
is disymmetric with respect to the axis of the Gaussian depletion …
Below is a test suggested by Mike Cullen (ecmrwf). The vorticity density exhibit a distorted non convex shape.
The Optimal Map (see the deformation of the grid below) has discontinuous derivatives.
