RayleighTaylor Instability

1
Rayleigh-Taylor Instability
Collaborators Vasily Zhakhovskii, M.
Horikoshi, K. Nishihara, Sergei Anisimov
2
Motivation
There are several phenomena that influence the
RTI and RMI. They include viscosity, thermal
conduction, thermodynamic non-ideality, surface
tension, etc. Usual hydrodynamic approach does
not take into account these effects.
Quantitative comparison with experiment
requires a different approach. One such example
provides the method of molecular dynamics.
3
Molecular Dynamics approach

• MD method is based on tracking of the atom
  motions by means of
• numerical solving Newtons equations
• MD method has great advantages over hydrodynamic
  methods
• Spatial mesh is not needed more
• EOS is not needed more
• The system under investigation can be far from
  local thermodynamic equilibrium
• Viscosity, heat conduction, surface tension are
  taken into account automatically
• Conservation laws are satisfied automatically
• MD method has the disadvantages (huge
  computational time)
• the total number of atoms
• so the system size 10TFLOPS)

4
Molecular Dynamics Simulation Technique
z
Lennard-Jones pair potential

• Potential
• barrier as
• piston

L J atoms
Fij
-X
X
gravity

• Periodical boundary conditions are
• imposed on the system along z-axis
• The atoms interact via Lennard-Jones (L-J) pair
  potential
• with cutoff at rc
• The piston is simulated by an external potential
  xi -X( fi )2

5
Initial Condition

• Density Ratio 21 (Atwood Number A 1/3)
• Number of Atom 12 millions (8 millions of light
  atoms)
• Gravity 1011 cm/sec2
• Initial Amplitude 0.06? Single Mode
• Space Size 1274 s 858 s 13.4 s
• Pressure profile variable
• Computational Resource Pentium?-S 1.4GHz 80
  (112GFLOPS)
• Computational Time Almost 2 weeks

6
Parallel Computing for load balancing.Dynamically
Re-distributed.
Actually atoms information was re-distributed.
Time Evolution
7
Time Evolution of Interface.Density profile.
heavy atoms
light atoms
?
Each pixel represents a small domain, which is
occupied approximately 50 atoms
8
Good Agreement with Theoretical Growthat linear
stage.
hExp(?t) where ?sqrt(AKg) L. Rayleigh (1900),
S.G. Taylor (1950)
9
The thickness of mixed layer
10
Conclusion

• We have developed the MD simulation code for RT
  instability.
• Parallelization for good load balancing by using
  re-distribution
• Simulation results agree with theoretical
  prediction.
• In the future
• More late time simulation (e.g., nonlinear
  regime)
• Making fully use of MD advantages (e.g.,
  analysis around singularity)
• New initial condition Hydro code does NOT
  detail

11
Interface evolution bydifferent hydro Schemes
Appendix
LL
CFLFh
JT
CLAW
WAFT
WENO
PPM
VH1
Ref http//www-troja.fjfi.cvut.cz/liska/CompareE
uler/compare8/