ALE and AMR Mesh Refinement Techniques for Multi-material Hydrodynamics Problems

Transcription

1 ALE and AMR Mesh Refinement Techniques for Multi-material Hydrodynamics Problems A. J. Barlow, AWE. ICFD Workshop on Mesh Refinement Techniques 7th December 2005

2 Acknowledgements Thanks to Chris Powell, Wayne Gaudin, Alan Dawes, Graham Ball, Dave Youngs and Andy Giles who have all supplied results of simulations and details of some of the methods they use.

3 Introduction Outline of talk Hydrodynamics problems The need for high resolution simulations Parallel computing v mesh refinement techniques Mesh movement v mesh topology change Mesh refinement techniques for Hydrodynamics problems ALE Eulerian AMR ALE/AMR Conclusions

4 Hydrodynamics problems AWE needs to be able to model shock hydrodynamics problems which involve solid materials under high strain rates generated by either high explosives or high power lasers. The numerical methods used need to be robust for high material deformation, capable of accurately modeling shocks and material interfaces, and preserve cylindrical symmetry. Mesh refinement techniques have been found to be important in delivering this capability. The main part of this talk will focus on these methods and how well they perform for hydrodynamics problems.

5 The need for high resolution Greater reliance is now being placed on simulation. Reduce cost experiments, some experiments can no longer be performed, to gain greater insight of physics involved etc This requires more predictive simulation codes and material models. The codes must be capable of performing simulations at significantly higher mesh resolution, both to improve accuracy and to fully exploit new material models. High resolution direct numerical simulations are also being used increasingly as part of a multi-scale modeling approach to develop more predictive material models for these simulation codes.

6 2 phase flow - Turbulence & Mixing 2D shock tube experiment Richtmyer - Meshkov instability at perturbed air/sf 6 interface Experiment 3D Calculation 2D Model

7 2 phase flow - turbulence & mixing 3D LES results - evolution of the mixing layer 1.6ms 2.5ms

8 Dynamic Friction 0.5 mm Deflection Micrograph 1 mm Simulation z z Plastic deformation confined to a thin layer at interface Thermal softening exceeds work hardening: strength decays

9 Dynamic Friction 0.5 mm Deflection Micrograph 2 mm Simulation z z Plastic deformation penetrates more deeply into aluminium Shear stress and elastic deformation also increase

10 Fracture Damage - 5 mm thick shell Plastic strain - 5 mm thick shell

11 Parallel v Mesh refinement Parallel computing Needs access to large HPC platform! Results identical however many processors are used. Significant gains for explicit algorithms provided sufficient work to do. Implicit algorithms required for some multi-physics simulations can limit parallel scalability. Mesh Refinement Techniques Significant gains possible without need for large HPC platform. Need to demonstrate results agree with uniform fine mesh simulations. Can limit parallel scalability. Both implicit and explicit algorithms benefit.

12 Parallel computing (1) Example: Freund problem on PEGASUS (3D SALE with slide)

13 Parallel computing (2) Example: Freund problem on HYDRA (3D Eulerian) Speed up 1024 Ideal 54M M 1 850k Processors

14 Mesh movement v mesh topology change Mesh movement Fixed mesh topology. Nodes moved to to refine some areas of problem at the expense of other parts of the problem. Easy to parallelise. No impact on parallel performance. Increase in mesh resolution limited (penalty method). Can degrade mesh quality and produce robustness problems. Mesh topology change Mesh topology changed by either changing mesh connectivity or adding and removing zones as required to focus resolution where and when it is required. Mesh resolution increase is effectively unlimited. Parallel performance can be degraded due to more complex data structures required and load balancing problems.

15 Arbitrary Lagrangian Eulerian (ALE) (1) CORVUS 2D multi-material ALE code Flexible multi-block unstructured mesh Distributed parallel Radiation hydro code Staggered grid Lagrange plus remap scheme. Predictor corrector time discretization. Finite element spacial discretization for Lagrangian step. Monotonic artificial viscosity.

16 Arbitrary Lagrangian Eulerian (ALE) (2) Two types of interface treatment slide lines and a multimaterial cell or VOF based treatment. Van Leer advection in volume coordinates for single material cells. Improved SLIC interface reconstruction method. Mesh adapted by moving nodes to improve mesh quality at the end of the Lagrangian step.

17 Mesh Movement Algorithms (1) Mesh Movement Philosophy Mesh movement philosophy applied to most applications is to strive to move the mesh with as close to Lagrangian mesh motion as possible. This naturally follows most flow features of interest such as shocks, material interfaces and steep gradients. Allows users to focus zoning in materials of interest. Mesh relaxation is then used in regions of high material deformation to improve mesh quality.

18 Mesh Movement Algorithms (2) The user defines how the mesh will move by applying a mesh movement algorithm to each mesh block. Winslow s equipotential relaxation method is used in most cases. Constraints can also be applied which typically keep a node Lagrangian until some condition is reached e.g. element quality criterian or physical condition is reached in surrounding elements. Separate movement algorithms are applied to nodes along sliding material boundaries.

19 Mesh Movement (1) Initial mesh for ICF capsule calculation

20 Mesh Movement (2) ICF capsule implosion with symmetric drive at 16.8 ns

21 Mesh Movement (3) ICF capsule implosion with asymmetric drive at 16.8 ns

22 Mesh Movement (4) Tantalum or aluminium foil Steel Aluminium Steel Dynamic Friction Experiment

23 Mesh Movement (5)

24 Mesh Movement (6) Dynamic Friction Experiment at s

25 Weighted Mesh movement Mesh movement can also be used to pull resolution into features of high importance. In CORVUS this is done by apply weights to materials or regions of high importance or applying weights to a particular flow variable such as density. The weights are applied to all the nodes within this material or region. A buffer zone is usually created by propagating the weights out a few zones then averaging the weights with neighbouring elements. This typically works well in delivering a doubling in resolution. But more extreme changes in resolution can lead to robustness problems.

26 Material weighted Mesh movement (1) Initial mesh for UK 10 Shaped Charge calculation

27 Material weighted Mesh movement (2) ALE calculation of UK 10 Shaped charge at s

28 Material weighted Mesh movement (3) Example - CORVUS simulation of projectile puncturing a water-filled container. Mesh deforms, but less than in Lagrangian case.

29 Density weighted mesh movement Example - CORVUS simulation of laser-driven flow

30 Parallel ALE mesh refinement Good parallel performance obtained for ALE mesh motion. Multi-material ALE calculation running to 4002s on a element mesh (1mm mesh resolution). Takes 16 hours CPU time on BlueOak to complete serial. Takes 40 CPU minutes to complete on BlueOak using 30 processors.

31 Dynamic friction recovery experiments FN6a - Explosively Driven Shear Measure subsurface deformation HE Aluminium Stainless Steel

32 Parallel ALE with anisotropic mesh refinement 60 2m calculations of FN6 ( elements) takes 18.5 hours to run serial, but can now be completed in 1438 CPU seconds using 60 processors on Blue OAK.

33 Parallel ALE with anisotropic mesh refinement mm background mesh with 4:1 refinement provides 60 2m resolution normal to the interface.

34 Eulerian Adaptive Mesh Refinement (AMR) (1) SHAMROCK 2D multi-material Eulerian AMR code Distributed parallel Builds on block patch AMR strategy developed by Berger and Quirk Staggered grid Lagrange plus remap scheme with VOF multi-material cell scheme and Youngs interface reconstruction and van Leer advection Radiation diffusion Solve for each patch iterate to converge temperatures on patch boundaries

35 Eulerian AMR (2) Error estimators used to drive mesh refinement Shocks and material interface kept at finest level initially. Now have option to derefine material interfaces later in problem. Artificial viscosity used to detect shock, second derivative for density and internal energy, burn fraction for reactive flow, pressure relative to Pcj for program burn. Significant gains in serial (~4-6 speed up) Parallel scalability is degraded by AMR Example - SHAMROCK AMR mesh showing patches added at material interfaces (initial configuration)

36 Eulerian AMR schemes (3) T=0 2s T=19 2s Example: shaped charge simulated by SHAMROCK T=100 2s

37 Eulerian AMR schemes (4) Example: laser-driven AGEX 2 experiment simulated on SHAMROCK (2D axisymmetric AMR) Shock wave with dynamic mesh adaption

38 ALE/AMR (1) ALE mesh movement techniques clearly provide a degree of mesh refinement. However, this is limited because the mesh topology is fixed and if it is used to agressively mesh quality and robustness will be reduced. A hybrid ALE/AMR method is under development for CORVUS to address this issue. Currently this is compatible with HE burn, slide, elasto-plastic flow and SALE.

39 ALE/AMR (2) A cell by cell refinement strategy has been adopted in contrast to the block patch approach that has been employed for AWE s Eulerian AMR code. Efficient data structures based on existing connectivity arrays. Disjoint nodes used at refinement boundaries for Lagrangian step and in applying mesh relaxation. Only solve on finest level. Advection uses ghosts to catch fluxes from fine to coarse.

40 ALE/AMR (3) Freund problem calculated with ALE/AMR at s.

41 ALE/AMR (4) Freund problem calculated with ALE/AMR at s.

42 Conclusions Mesh refinement techniques are clearly vital in moving towards more predictive simulation codes for simulating shock hydrodynamics problems. Some of the relative merits of the different mesh refinement techniques has been discussed. Recent progress at AWE in developing ALE mesh movement techniques and adaptive mesh refinement techniques and recent work to produce a hydrid code which exploits both techniques. The importance of being able to parallelise codes which exploit these techniques without loosing parallel efficiency has also been discussed.