Jean-François Remacle



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



Stephanie Remacle-Landrain