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Simulation of Multi-material Flows Using Adaptive Mesh Refinement Technology

Explore a cutting-edge numerical model integrating high-order methods, interface reconstruction, advanced equations of state, and adaptive mesh refinement for accurate shock wave processes simulation. Implementing new physics like thermal conductivity, electromagnetic fields, and ionization. Future plans include further physics implementations.

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Simulation of Multi-material Flows Using Adaptive Mesh Refinement Technology

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  1. Simulation of Multi-material Flows Using Adaptive Mesh Refinement Technology M. Povarnitsyn, K. Khishchenko, P. Levashov, A. Zakharenkov Joint Institute for High Temperatures RAS, Moscow, Russia povar@ihed.ras.ru New Models and Hydrocodes for Shock Wave Processes in Condensed Matter, Lisbon – Monte Estoril, Portugal 18-23 May, 2008

  2. Outline • Introduction • Numerical model • Basic equations • Interface reconstruction • Equation of state • Adaptive mesh refinement • Results of simulation • Conclusions and future plans

  3. Numerical model • Multi-material high-order Godunov’s method in Eulerian form (Miller & Puckett, J. Comp. Phys., 1996) • Interface reconstruction algorithm (Youngs) • Multiphase equations of state (Khishchenko) • Adaptive mesh refinement (Chombo, LBNL)

  4. Multi-material Eulerian hydrodynamics f2 Mixture model f1 f3

  5. j+1 U*t j j-1 i i+1 i-1 U* Interface reconstruction algorithm 2D 3D (b) (a) (d) (c) D. Youngs (1987) D. Littlefield (1999) Symmetric difference approximation or some norm minimization is used to determine unit normal vector (e) Specific corner and specific orientation choice makes only five possible intersections of the cell

  6. kinetic models Semi-empirical thermal EOS Metastable EOS Stable EOS bn bn sp “instant relaxation”   0 “frozen relaxation”   

  7. Ti - Al impact at 10.4 km/s Experiment: Chhabildas et al. Int. J. Impact. Eng. 2006; 33: 158-68. Ti Al V=10.4 km/s

  8. liquid + gas Thermal decomposition of metastable liquid Metastable liquid separation into liquid-gas mixture V. P. Skripov, Metastable Liquids (New York: Wiley, 1974).

  9. Model of homogeneous nucleation 0.9Tc<T<Tc V.P. Skripov, Metastable Liquids (New York: Wiley, 1974).

  10. Mechanicalspallation (cavitation) P P P liquid + voids Time to fracture is governed by the confluence of voids

  11. Spallation criteria Minimal possible pressure P P < -Y0 Energy minimization P P D. Grady, J. Mech. Phys. Solids 36, 353 (1988).

  12. Adaptive mesh refinement (AMR)

  13. Recursive integration in time Δt/4 Δt/2 Δt/4 Δt Δt/4 Δt/2 Δt/4

  14. Pb on Al impact at 5 km/s

  15. Evolution of meshes

  16. Pb on Al impact at 5 km/s Pb on Al at 5 km/s 5 levels grid2048 х 2048 12 procs

  17. Multi-material Godunov’s framework with AMR Pb, Al and air 5 levels grid 1024х1024 10000 particles100 mkm 12 procs

  18. AMR effectiveness 9000 Run time, s 8000 7000 6000 AMR with 3 levels 5000 Equivalent mesh 4000 3000 2000 1000 Physical time,mks 0 0 0.2 0.4 0.6 0.8 1.0 1.2

  19. Two-temperature multi-materialEulerian hydrodynamics Basic equations Mixture model

  20. Conclusions and Outlook • Implementation of high-order multi-material Eulerian model into AMR was performed • Usage of metastable and stable equations of state allows to take into account kinetics of decomposition of metastable phases • Time-dependent criteria of cavitation in metastable liquid state were introduced into hydrodynamic model • Implementation of new physics (thermal conductivity, electro-magnetic field, ionization) is underway

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