1. Multiphase Flow in ALE3D
Presented by:
David Stevens
Lawrence Livermore National Laboratory
UCRL-PRES

2. Introduction to multiphase flow
Spherical Charge
Figure 3 from Fan Zhang et. Al., “Explosive Dispersal of Solid Particles”, Shock Waves, 11, , 2001.
High speed photographs of a 10.6 cm radius charge
Frames separated ms
The goal is to develop a numerical method capable of accurately capturing such shock/turbulence interactions.

3. The Multiphase Equations (2-Phase)
High particle number concentrations often preclude the use of stochastic particle techniques.
The continuum two-phase model of Baer and Nunziato (SNL) with modifications form the basis of the implementation.
Each phase is described by evolution equations for mass, momentum, internal energy and volume fraction.

4. The Treatment of the Multiphase Interactions
The Hydrodynamic phase is composed of a nodal ALE phase and a species Riemann update.
The model equations are time-split into a pure hydrodynamic phase and a multiphase relaxation phase.

5. The zonal Riemann update for species quantities
A Riemann solver is used to evaluate the species quantities.
The Riemann solve is just a new “edge state” formalism that replace the original upwind “edge state” formalism of the Van Leer based advection for zonal scalars remap.
Edge states from the advection are cached and converted into fluxes. The combination of a Van Leer predictor followed by a Riemann solve corrector is a standard second-order formalism.

6. V&V for multiphase model
One Dimensional test cases
Andrianov’s analytic solutions
Rogue et al’s shock tube.
Water/air shock tube.
Multi-dimensional test cases
Zhang particle dispersion experiments (DRDC).
Applied Problems
Particle dispersion.
Particle Jets.
DDT.
Deflagration modes in HE and propellants.

7. Method Comparison on the Water-Air Shock Tube
High pressure liquid expanding into low pressure air.
Challenging problem due to the wide range in densities and sound speeds.
Several Riemann Solvers have been compared.
Rusanov is a single wave solver.
ASW and AUFS are seven wave Riemann solvers.
The presence of a predictor appears to outweigh the full amount of terms in the predictor.

8. Under the hood: The Lagrangian system of primitive variables

9. Rogue Shock Tube
At left is Figure 11 from Rogue, Rodriguez, Haas, and Saurel’s: “Experimental and numerical investigation of the shock-induced fluidization of a particle bed, Shock Waves, 8, 29-45, 1998.
This is a series of shadowgraphs of a 2 mm bed of nylon beads being accelerated by a Ma 1.3 shock. Each panel represents a different time in the experiment..

10. The Rogue Shock Tube Above is Figure 15 from Rogue, et al.
Top left is the particle cloud density at 100 us.
Bottom right is the gas pressure.

11. Initial Rogue Shock Tube Comparison
Numerical results agree well with the experimental data.
The simulated fluidized bed is slightly ahead of the experimental observations.

12. Deflagration to Detonation Transition
The multiphase model has replicated the experimental and simulation results from Baer et al., Combustion and Flame, 65, 15.
Detonation Front speeds agree with observations and Mel’s original simulations in both the convective, compressive and detonation regions of the flow.
5.3
1.1
0.5

13. Improved Numerics and Mesh Resolution (AMR)
Adaptive mesh refinement is one method for achieving high resolution without imposing O(n4) growth in computational requirements.
Following are simple examples from prototype 1D and 3D shock physics simulations using a combined ALE3D/SAMRAI model.
Mathew Dawson (DHS Summer Intern, 2005) examined the role of:
Numerical method
Number of elements
Refinement levels
Refinement factor
Mesh efficiency

14. Improved Numerical Methods
Traditional methods efficiently track shocks
Improved methods required for accurate modeling
Actual fluid motion
Contact discontinuities
HLL, typical numerical method used in production models
Carbuncle instability and spurious sollutions
HLL/C efficient and robust but adds excessive diffusion around contact discontinuities
Artificially upstream flux vector splitting (AUFS)
Robust, feasible, reliable
Provides resolution on discontinuities and clean solutions
Avoids carbuncle instability and kinked mach stems
The following 3D results focus on the second-order predictor-corrector AUFS model

15. Numerical Method Comparison Shock Tube Analysis
With increasing resolution, AUSF exhibits dramatically better convergence for contact discontinuities
AUSF
HLL
Rusanov
AUSF
HLL
Rusanov
Density comparison for 200 zones.
Contact discontinuity at 200 zones.

16. Local versus Global Mesh Refinement
Local mesh refinement is able to preserve the gains observed with AUSF when compared with global mesh refinement.
NX 50
NX 100
NX 200
NX 400
Level 1
Level 2
Level 3
Level4

17. Preferred Numerical Directions
Rectangular meshes tend to imprint directional character on spherical problems
This problem is influenced by both the numerical method and the accuracy used
Higher refinement reduces this problem
Further evaluation is required when SAMRAI multiblock capacities are brought online
Lineouts at 30, 45, and 60 degrees
Cross-section of density field

18. Gradient Resolution Gradients in 3D are prone to smearing
Mitigation of gradient diffusion achieved through increasing refinement
Density gradient larger for a tangent lineout as radial resolution increases.
NX 50
NX 100
Density lineout tangent to shockwave
Density 2D slice using HLL Solver (NX =100)
Density 2D slice using HLL Solver (NX =50)

19. High performance Computing
Simulations on 3600 processors were completed successfully
Demonstrating robustness of code
Optimal refinement parameters in 3D
Based on computational efficiency
Overall interface and operation capability
3D Display of zones and corresponding levels with density slice
3D Display magnified with enhanced zones on the left

20. Conclusions And Future Developments
Multi-wave Riemann solvers exhibit more accurate results on many Multiphase problems.
This performance is reduced by a lack of robustness on more complex problems.
Transition to turbulence studies:
Rayleigh-Taylor, Richtmyer- Meshkov instabilities
Multilevel, multiphase V&V.
Deflagration to Detonation studies (DDT)
Dynamically fluidized beds.