Large deformation modelling in geomechanics

LBM-DEM, MPM, LEM, and Devops


Krishna Kumar, kks32@cam.ac.uk
University of Cambridge




University of California, Berkeley
26 September 2016.

Multiscale modelling in geomechanics

Cambridge-Berkeley computational geomechanics

  • Lattice-Boltzmann + Discrete Element Method
  • Finite Element Method - Thermo-Hydro Mechanical Coupling
  • Material Point Method
  • Lattice Element Method
View the CB-Geo website for more information and software tools

Landslides: dissipation mechanism

Collapse in fluid: Set-up

LBM - DEM simulation of granular collapse in fluid




aspect ratio 'a' of 6

Lattice Boltzmann - MRT

Real Fluid vs LBM Idealisation
LBM D2Q9 Model

\[f_{i}(x + dx, t +\Delta t) - f_{i}(x, t) = -S_{\alpha i}( f_{i}(x, t) - f_{i} ^ {eq}(x, t))\]
  • $S_{\alpha i}$ is the collisional matrix.
  • Probability density of finding a particle : $f(x,\varepsilon, t) $, where, x is position, $\varepsilon$ is velocity, and t is time.
Streaming
Collision

LBM-DEM fluid-solid coupling

$$\Delta t_{s}=\frac{\Delta t}{\mathit{n}_{s}} \qquad (\mathit{n}_{s}=[\Delta t/ \Delta t_{D}]+1) $$
  • At every fluid iteration, $\mathit{n}_{s}$ sub-steps of DEM iterations are performed using the time step $\Delta t_{s}$.
  • The hydrodynamic force is unchanged during the sub-cycling.

LBM laminar & turbulent flows

Lattice Boltzmann

CFD
Poiseuille Flow

Smagorinsky model (LES):

$\nu_{s}(x,t)=(C_s \Delta)^2\sqrt{S_{ij}S_{ij}} \mbox{ ; } S_{ij}=\frac{1}{2}(\frac{\partial u_i}{\partial x_j}+\frac{\partial u_j}{\partial x_i})$
Karman Vortex Street

Granular collapse in fluid: Effect of aspect ratio



aspect ratio 'a' of 0.4

aspect ratio 'a' of 4

Collapse in fluid: Effect of permeability


Reduction ‘R’=0.7r

Reduction ‘R’=0.9r

Collapse in fluid: Effect of permeability

Dirichlet boundary conditions constrain the pressure/density at the boundaries (Zou and He, 1997)
$\rho_0=\sum_{a}f_{a} \mbox{ and } \textbf{u}=\frac{1}{\rho_0}\sum_{a}f_{a}$

Reduction in radius
LBM-DEM Permeability and Theoretical Solutions

Collapse in fluid: Effect of permeability


Reduction ‘R’=0.7r

Reduction ‘R’=0.9r

Collapse in fluid: Effect of permeability

Effect of permeability: stress

Effect of permeability: runout

Effect of permeability: kinetic energy

Effect of permeability: runout

CPU v GPU

LBM - DEM a = 0.8 & 10,000 partilces



  • LBM Nodes = 50 Million : DEM grains = 10000 discs
  • Real-time = 2 seconds
  • Run-time = 4 hours
  • Speedup = 25x on a Tesla K20

LBM - DEM: Road map

  • Generic templatised C++11/14 code
  • Live rendering of VTK using GPUs (inprogress)
  • Multi-GPU support across nodes
  • LBM:
    • 3D LBM model
    • 3D LB - DEM coupling
    • Two-phase LBM fluid flow
  • DEM:
    • 3D DEM with different shapes
    • DEM simulations on GPU
    • Contact models for DEM
    • Special boundaries for DEM
    • Simulating billion DEM particles
Simulating millions of DEM particles

Mesh-based vs Mesh-free techniques

Material Point Method

Porosity in MPM

Material Point Method

MPM v DEM column collapse

a = 0.4
a = 6

DEM column collapse

MPM v DEM column collapse

Run-out v aspect ratio

MPM slope failure

MPM v DEM run-out slope v collapse

Run-out v aspect ratio

Lattice Element Method

Lattice Element Method - Fluid coupling

  • First assume injection pressure $P_{in}$ and injection rate $Q_{in}$ at injection point
  • Solve fluid pressure at each fluid node
  • Convert pressure to node force and solve LEM to update fracture aperture
  • Repeat the above process until convergence
$$q = - \frac{h^3}{12\mu}\frac{dp}{dx}$$

LEM hydraulic fracturing

John Wong, University of Cambridge

Software development

  • Git
  • Continous integration
  • Unit testing
  • Container technology

Git

  • Git is a distributed version control system that keeps track of your changes.
  • Git only stores the ‘delta’, i.e., only the difference between the previous version and the current version, so it doesn’t take up lots of valuable hard disk space. Git also compresses your file
  • GitHub, GitLab, BitBucket, ...

Continous Integration

  • Builds: Multiple compilers and optimisations
  • Unit testing
  • Benchmarks
  • Formatting - clangformat
  • Coverage analysis
  • Static analysis
  • Continous delivery - Deployments

Unit testing

  • Test every function
  • Test for all possible values
  • C++ unit testing frameworks:
    • Catch
    • Google mock test
    • Boost unit test

All tests passed (36 assertions in 3 test cases)

Docker containers

  • Automates the deployment of applications by packaging an application with all of its dependencies into software containers.
  • Docker containers wrap up a piece of software in a complete filesystem that contains everything it needs to run: code, runtime, system tools, system libraries – anything you can install on a server.
  • This guarantees that it will always run the same - Research reproducability

Software development: Roadmap

  • Opensource development
  • Modular code development
  • HDF5
  • In memory databases
  • Apache Spark - MapReduce
  • Version control
  • Unit testing
  • Continous integration and deployment
  • Docker container - Kubernetes

Thank you!!


Krishna Kumar, kks32@cam.ac.uk