2D Rayleigh Taylor.
Transient computation of unstable flows provide an application where adaptivity
in time is crucial. The instability of an interface separating miscible fluids
of different densities subject to gravity is known as a
Rayleigh-Taylor Instability. Bubbles (spikes) of lighter (heavier)
fluid penetrate into the heavier (lighter) fluid, leaving behind a region
where the two fluids are mixed. This mixing region quickly becomes irregular
and may provide an understanding of turbulence since the flow there has
chaotic features.
 
 
 
 
Density contours at different times for the Rayleigh Taylor Instability
This simulation was performed on a 4 processor intel machine using a non conforming
adaptive grid method and our
Discontinuous Galerkin code.
An animation of both density and mesh evolutions is available
here . This next
animation shows the evolution of the fluid density for the 1-mode
Rayleigh-Taylor with 2 different refinements.
3D Rayleigh Taylor.
We have also computed 3D Rayleigh Taylor instabilities on large scale computers like
on
lemieux or
Blue Horizon .
 
Isosurface of density for a 1-mode and 10-modes 3D Rayleigh Taylor Instability
2D Vortex Sheets.
We consider a square domain of size 1 X 1 centered at
x=0 and y=0. The problem is initially divided into four
quadrants. Quadrant 1 is the upper right, 2 the upper
left, 3 the lower left and 4 the lower right. All boundary
conditions are transmitting (we copy the interior data perpendicular
to the boundary). We initialize each quadrant with the following
values for u {density,x velocity, y velocity, pressure}.
quantities :
Quadrant 1 : u = {1.0, 0.75,-0.5,1.0}        
Quadrant 2 : u = {2.0, 0.75, 0.5,1.0}
Quadrant 3 : u = {1.0,-0.75, 0.5,1.0}       
Quadrant 4 : u = {3.0,-0.75,-0.5,1.0}
In this problem four contact discontinuities are rotating around the
center of the square creating vortex sheets.
An animation of
density and mesh
evolutions are available.
Density contours for the vortex sheet
For the same problem, we tryed a anisotropic mesh refinement. What follows is a 8 hours run on one processor,
using anisotropic mesh refinement. An animation can be found
here
Four Contacts, anisotropic refinement