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Computer Practical: Numerical Gasdynamics Richtmyer-Meshkov Instability Group 6

Computer Practical: Numerical Gasdynamics Richtmyer-Meshkov Instability Group 6 Comparison of Results with Different Grid Points 2 nd Order Roe Naseem Uddin Lucy Gray. Richtmyer-Meshkov Instability. Introduction Results Conclusions Questions?. Richtmyer-Meshkov Instability

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Computer Practical: Numerical Gasdynamics Richtmyer-Meshkov Instability Group 6

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  1. Computer Practical: Numerical Gasdynamics Richtmyer-Meshkov Instability Group 6 Comparison of Results with Different Grid Points 2nd Order Roe Naseem Uddin Lucy Gray

  2. Richtmyer-Meshkov Instability • Introduction • Results • Conclusions • Questions?

  3. Richtmyer-Meshkov Instability Introduction: Definition “The Richtmyer-Meshkov instability arises when a shock wave interacts with an interface separating two different fluids.” • Theoretically Predicted: Richtmyer 1960 • Experimentally observed: Meshkov 1969 • Simulation: Good test case for: • CFD validation. • Investigation into effects of differing parameters on results, e.g, grid size, time step size, flux functions… etc…

  4. Richtmyer-Meshkov Instability Introduction: Basic configuration • Two fluids initially at rest with differing properties, e.g. different densities • Separated by interface with an initial perturbation • Normal shock wave ( travelling from top to bottom from Fluid 1 into Fluid 2) shock interface From: M. Brouillette, The Richtmyer-Meshkov Instability, Annu. Rev. Fluid Mech. 34, 445-68 (2002)

  5. Richtmyer-Meshkov Instability Introduction: Development • Initial configuration • Linear growth with time – crests and troughs are symmetric • Start of nonlinear evolution – asymmetric spike and bubble development • Roll-up of spike • Emergence of small-scales and turbulent mixing From: M. Brouillette, The Richtmyer-Meshkov Instability, Annu. Rev. Fluid Mech. 34, 445-68 (2002)

  6. Richtmyer-Meshkov Instability Simulation: Euler 2D code • MUSCL Technique • 2nd Order in space & time • Temporal evolution & spatial reconstruction • Eulerian remapping & slope limiting (minmod)

  7. Richtmyer-Meshkov Instability Results: Computing Time

  8. Richtmyer-Meshkov Instability Structure details – Generated Vortices Coarse grid simulation The vortex structures are due to baroclinic vorticity at the interface. 0 time step 20 time steps 60 time steps 100 time steps

  9. Vortices are only clear with fine grids Secondary vortex Mushroom shaped vortex

  10. Richtmyer-Meshkov Instability Structure details Generated Vortices Fine Grid Simulation Two pairs of counter rotating vortices in the Mushrom-shaped structure. As time increases two more counter rotating structures appear.

  11. Structure details – mesh comparison Fine Coarse 0 time step 20 time steps 40 time steps

  12. Richtmyer-Meshkov Instability Conclusion: Structure details • Limited spatial resolution  failure to resolve smaller scales Further Work: • Effects of flux function on structures • Expansion to 3D • Expectation of different structures

  13. Thank you for your attention. Further questions?

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