SNAC: a tutorial. Eunseo Choi. July 29, Lamont-Doherty Earth Observatory

Transcription

1 SNAC: a tutorial Eunseo Choi Lamont-Doherty Earth Observatory July 29, 2010

2 What is SNAC? StGermaiN Analysis of Continua 2 of 20

3 What is SNAC? StGermaiN Analysis of Continua 3-D Version of FLAC 2 of 20

4 What is SNAC? StGermaiN Analysis of Continua 3-D Version of FLAC Essentially, dynamic, explciit, and Lagrangian finite element code with linear tetrahedral elements. 2 of 20

5 Governing Equations Principle of virtual power in dynamic form ( 0 = δv ρ v ) dω (δv) : σdω δvρgd Ω Ω t Ω Ω Heat energy balance. 3 of 20

6 Discrete Equations Local equilibrium on a node a t n+ t = 1 M (Ft n int + F t n ext ) Forward Euler (explicit) M v = F int + F ext = F res v(t + t) = v(t) + t F res M Updated Lagrangian x(t + t) = x(t) + tv(t) No matrix assembly. 4 of 20

7 Then, why called finite difference code?? Algebraic approximation to partial derivatives. No shape functions. f,i dv = fn i dγ, (1) Ω Ω f,i = 1 fn i dγ, (2) V Ω 5 of 20 f,i = 1 V = 1 3V = 1 3V 4 f l ni l A l = 1 V l=1 4 m=1 f m 4 l=1, =m l=1 n l i A l 4 f m ni l A l m=1, =l 4 f m ni m A m, (3) m=1

8 Features 3-D, MPI-parallel, domain decomposition. All supported by StGermain. Decent performance known up to 4K cores. Force damping for static/steady state equilibrium. Remeshing for large deformation ( Lagrangian). Conditionally stable ( explicit) but large time step allowed through Mass scaling. Mixed discretization for incompressibility and symmetric response. Easy to implement non-linear rheologies: No need for consistent tangential stiffness. Verified through benchmarking. 6 of 20

9 Benefits from StGermain StGermain Sofrware framework for scientific applications. Provides sustainable, collaborative computational development environments. Written in C. ( Benefits Input file in XML format: Logical organization of parameter. Modular: Can try things without compiling the whole code and by changing input files only. Various BC including user-defined functions. Switching between rheologies. Generation of structured mesh. Optimized domain decomposition. 7 of 20

10 Mixed Discretization Structured hexahedral mesh two sets of linear tetrahedra. ɛ ij = θδ ij + e ij, where θ = ɛ ii /3. θ of each tet is replaced with. θ 1 N tet N tet θ n n=1 Two equivalent overlays are required for symmetric response. 8 of 20

11 Mixed Discretization <How bad it can be without M.D.: 2-D Example> 9 of 20

12 Mixed Discretization <How bad it can be without M.D.: 2-D Example> <Lucky Mesh> 9 of 20 <Bad Mesh>

13 Mixed Discretization <Results from the Lucky mesh> <Results from the Bad mesh> 10 of 20

14 Elasto-Visco-Plastic Rheology η = η(t, σ, ɛ): Effective viscosity approach for creep. η : Mohr-Coulomb plasticity. σ Y : Maxwell viscoelasticity. Brittle and plastic(creeping) regimes do not need to be pre-determined. 11 of 20

15 Remeshing <Field interpolation> Blue: Deformed, Red: Remeshed <Superconvergent Patch Recovery> 12 of 20

16 SNAC and GALE Basis GALE SNAC FEM solving momentum balance (quasi-)statically Time marching Meshing Specific Technique Implicit Structured (no need for complex mesh) PIC/ALE Explicit Structured (more flexibility desired) Remeshing Rheology Viscoplastic Elasto-visco-plastic 13 of 20

17 SNAC and GALE Large deformation Prediction of structural evolution GALE Yes SNAC Yes, by accumulating small strain. Yes Free surface Yes with air layer Yes by free surface Tracking interface Yes suffers numerical diffusion Multi-physics Diking, erosion Thermal stress, simple erosion 14 of 20

18 Challenges Optimization for improved performance Parallel performance is fine, but the overall efficiency needs improvements. More sophisticated multi-physics e.g., melting and melt migration, fully coupled thermomechanics. More realistic rheology Rate-dependent plasticity, damage models, various creep mechanisms. Mesh- and resolution-dependence of localization Embedding weak/strong discontinuity is one solution. Reducing remeshing-induced diffusion: Particles? 15 of 20

19 To help and be helped... send s to or with explicit titles. Please post questions, bug reports, feature requests, other suggestions, etc. 16 of 20

20 Preparation How to get it: SNAC, libxml2, mpi, GNU Scientific Library. How to build it:./configure.sh; make. Consider optimization option: --options=optimised. 17 of 20

21 How to run it Environment setup command line Basics of XML input file simulation control plugins: what are available, how to load one. material properties IC/BCs 18 of 20

22 Post-processing 19 of 20

23 Advanced topics How to extend the capabilities: Modifying 20 of 20