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?