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 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…

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) From: M. Brouillette, The Richtmyer-Meshkov Instability, Annu. Rev. Fluid Mech. 34, (2002) interfaceshock

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

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

Richtmyer-Meshkov Instability Results: Computing Time Grid size:coarsefineRatio (fine:coarse) 300 x x 3964 Computing Time: sec sec8.4 CPU time:2 808 sec sec Intel Pentium single processor 512 MB Ram, 1.6 GHz 6

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

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

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

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

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

Thank you for your attention. Further questions?