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 Newton’s equations  MD method has great advantages over hydrodynamic methods: 1.Spatial mesh is not needed more 2.EOS is not needed more 3.The system under investigation can be far from local thermodynamic equilibrium 4.Viscosity, heat conduction, surface tension are taken into account automatically 5.Conservation laws are satisfied automatically  MD method has the disadvantages : (huge computational time) 1.the total number of atoms < 10^8 so the system size < 1 um (needs over 10TFLOPS)

4 Molecular Dynamics Simulation Technique Periodical boundary conditions are imposed on the system along z-axis The atoms interact via Lennard-Jones (L-J) pair potential with cutoff at r c The piston is simulated by an external potential ~[ x i -X( φ i )] 2 Potential barrier as piston L J atoms F ij z -X Lennard-Jones pair potential X gravity

5 Initial Condition Density Ratio 2:1 (Atwood Number; A =1/3) Number of Atom 12 millions (8 millions of light atoms) Gravity 10^11 cm/sec^2 Initial Amplitude 0.06λ & Single Mode Space Size 1274  × 858  × 13.4  Pressure profile variable Computational Resource: Pentium Ⅲ -S 1.4GHz * 80 (112GFLOPS) Computational Time: Almost 2 weeks

6 Parallel Computing for load balancing. Dynamically Re-distributed. Time Evolution Actually atom’s information was re-distributed.

7 Time Evolution of Interface. Density profile. λ light atoms heavy atoms Each pixel represents a small domain, which is occupied approximately 50 atoms

8 Good Agreement with Theoretical Growth at linear stage. h~Exp(γt) where γ=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 by different hydro Schemes CFLFhJT LL CLAW WAFTWENOPPMVH1 Ref: Appendix