Rock Mechanics and Rock Engineering

, Volume 52, Issue 10, pp 3675–3690 | Cite as

A Coupling Model of Distinct Lattice Spring Model and Lattice Boltzmann Method for Hydraulic Fracturing

  • Chao Jiang
  • Gao-Feng ZhaoEmail author
Original Paper


In this work, the distinct lattice spring model (DLSM) and the lattice Boltzmann method (LBM) are coupled together to simulate hydraulic fracturing problems. As the DLSM and LBM are both lattice modelling methods, the lattice meshes in these two systems are simply overlapped, which results in the same resolution in both the DLSM and LBM. The momentum exchange bounce-back algorithm is used to evaluate the forces exerted on the solid particles. Moreover, the calculation step in the LBM and DLSM is synchronised for prompt updates of fluid–solid interactions. The coupled model is further validated through a series of benchmarks. Finally, the coupled model shows its ability to simulate hydraulic fracturing in formations with complex discrete fracture networks.


Hydraulic fracturing Distinct lattice spring model Lattice Boltzmann method 

List of symbols

Roman alphabets


One of the nine directions of the D2Q9 model


The opposite direction of α


The velocity-coupling factor from the DLSM to LBM


The force-coupling factor from the LBM to DLSM


The half-channel width


The basic speed on the lattice


The speed of sound in the lattice


The spatial dimension of the analysis


The pressure gradient


The body force term


The particle distribution function


The equilibrium distribution


The wall correction factor of the drag force


The length of the lid-driven cavity


The length scale factor of the DLSM to a physical system


The length scale factor of the LBM to a physical system


The macroscopic pressure


The Reynolds number


The macroscopic density


The density scale factor of the DLSM to a physical system


The density scale factor of the LBM to a physical system


The initial density of the LBM


The far-field stresses from north or south


The far-field stresses from east or west


The time-scale factor of the DLSM to a physical system


The time-scale factor of the LBM to a physical system


The ratio of the diameter of the cylinder to the width of the channel

\(u_{\hbox{max} }\)

The maximum velocity approaching the cylinder


The dynamic viscosity


The flow velocity in the X direction

Greek symbols

\(\Delta t\)

The time step

\(\Delta x\)

The lattice space width



This research is financially supported by the National Natural Science Foundation of China (Grant No. 1177020290).


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Hydraulic Engineering Simulation and Safety, School of Civil EngineeringTianjin UniversityTianjinChina
  2. 2.School of Civil and Environmental EngineeringThe University of New South WalesSydneyAustralia

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