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Development of a Coupled 3-D DEM-LBM Model for Simulation of Dynamic Rock-Fluid Interaction

  • Author(s): Gardner, Michael Henry
  • Advisor(s): Sitar, Nicholas
  • et al.
Abstract

Scour of rock is a challenging and interesting problem that combines rock mechanics

and hydraulics of turbulent flow. On a practical level, rock erosion is a critical issue facing

many of the world’s dams at which excessive scour of the dam foundation or spillway can

compromise the stability of the dam resulting in significant remediation costs, if not direct

personal property damage or even loss of life. The most current example of this problem is

Oroville Dam in Northern California where massive scour damage to both the service and

emergency spillways during the flood events of February 2017 led to the evacuation of more

than 188,000 people living downstream of the dam.

This research is specifically aimed at developing the ability to numerically evaluate rock-

water interaction, building upon the experimental and analytical work by George and Sitar

. The focus is on producing simulation techniques capable of consid-

ering the interaction between three-dimensional polyhedral rock blocks interacting with fluid

such that the complex shape of the blocks is captured in both the fluid and solid numerical

models. Accounting for the rock block geometry and orientations is essential in capturing

the correct kinematic response.

To this end, a three-dimensional, open-source program to generate the fractured rock

mass was developed based on a linear programming approach. The application runs on

Apache Spark which enables it to run locally, on a computer cluster or on the Cloud. The

program automatically maintains load balance among parallel processes and can be scaled

up to meet computational demands without having to make any changes to the underlying

source code. This enables the program to generate real-world scale block systems containing

millions of blocks in minutes.

The second stage of this research effort focused on developing a new open-source Discrete

Element Method (DEM) program capable of analyzing the kinematic response of fractured

rock. The contact detection computations for DEM are also based on a linear programming

approach such that similar logic and data structures can be used in both the block generation

and DEM code, though the DEM code is written in C++. The program was validated against2

analytical solutions as well as other numerical solutions and has been shown to accurately

capture the kinematic response of three-dimensional polyhedral rock blocks.

The DEM formulation was then extended to perform coupled fluid-solid interaction anal-

yses by coupling it with the weakly compressible Lattice Boltzmann Method (LBM). A

new algorithm, which extends the partially saturated approach, was developed to consider

three-dimensional convex polyhedra moving through the fluid domain. The algorithm uses

both linear programming and simplex integration for the coupling process. The LBM code

and the new fluid-solid coupling algorithm were validated against experimental data and

the capabilities of the new coupled DEM-LBM implementation were explored by evaluating

the performance of the program in simulating several different problems involving fluid-solid

interaction. The results show that the program is able to accurately capture the interaction

between polyhedral rock blocks and fluid; however, further performance improvements are

necessary to simulate realistic, field scale problems. Particularly, adaptive mesh refinement

and multigrid methods implemented in a parallel computing environment will be essential

for capturing the highly computationally intensive and multiscale nature of rock-fluid inter-

action.

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