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Computer Practical: Numerical Gasdynamics
Richtmyer-Meshkov Instability
Group 6
Comparison of Results with Different Grid Points
2nd 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, 445-68 (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, 445-68 (2002)
Richtmyer-Meshkov Instability
Simulation: Euler 2D code
–MUSCL Technique
–2nd Order in space & time
–Temporal evolution & spatial reconstruction
–Eulerian remapping & slope limiting (minmod)
Richtmyer-Meshkov Instability
Results: Computing Time
Grid size: coarse fine Ratio (fine:coarse)
300 x 198 600 x 396 4
Computing Time:
1318.98 sec 11138.5 sec 8.4
CPU time: 2 808 sec 16 884 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
x
y
25 30 35
28
30
32
34
36
38
40
42
Two pairs of counter rotating vortices in the Mushrom-shaped structure.
x
y
20 25
28
29
30
31
32
33
34
35
36
37
38
39
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?
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