Smoothed Particle Hydrodynamics

Exploring the method of smoothed particle hydrodynamics (SPH) and its application to iceberg­ capsize dynamics

Lynn Kaluzienski, 9/20/2015, University of Maine

Analytical solutions for problems in fluid dynamics are unavailable for most real world flows. The method of Smoothed Particle Hydrodynamics (SPH) was initially developed for astrophysical problems and has since been used to formulate approximate solutions for equations in fluid dynamics, chiefly the Navier Stokes solution for a weakly compressible fluid. SPH takes the innovative approach of replacing a fluid with an array of particles and solving the Navier Stokes equation on a particle by particle basis. A smoothing function is applied to each individual particle to determine the influence of its neighbors within a certain radius giving more weight to nearby particles. SPH is naturally a mesh­free Lagrangian method, providing several benefits over former grid­based techniques in capturing surface accelerations and removing the need of tracking fluid boundaries. One difficulty with the SPH method is the need for a large quantity of particles to achieve the same precision as a grid­based approach. However, recent improvements in computational power such as the widespread use of graphic processing units (GPUs) have made SPH implementation feasible and computationally inexpensive. Several open source codes, such as DualSPHysics, make high resolution SPH simulations easily achievable on computers with multiple GPU processing units. Depending on complexity, several hundred thousand particle simulations can be achieved on the order of minutes to hours on a desktop computer. Larger­scale models with millions to even billions of particles can be efficiently computed on supercomputers. The University of Maine SECS Numerical Laboratory currently has SPH simulations running on multiple GPUs. In addition, our collaboration with the Advanced Computing Group at Umaine will allow us to run increasingly complex and higher resolution simulations on one of their supercomputers in the near future.

In this model a fluid is initially held in a square configuration along a sloped ramp with open boundaries on both sides. At the the first time step the fluid is allow to flow outward due to the force of gravity and begins to flow down the ramp. Once the fluid particles meet the boundary edge on the right they cross over to the left side of the ramp. During the first few time steps the fluid quickly moves to fill the void on the upper left hand side and crashes with slower moving particles creating a significant splashing effect and the formation of a standing wave. Throughout the simulation this standing wave begins to die out as the flow approaches a state of equilibrium.

In this model a fluid is initially held in a block configuration. At the first time step the fluid is allowed to flow out due to the force of gravity. As if flows outward it crashes into a rectangular block and interacts with the boundary walls. The color of each fluid particle corresponds to its velocity magnitude (m/s) at each time step.

Animations from SPH on front page ­Periodic Boundary Conditions

­­Click on video and takes to Smoothed Particle Hydrodynamics page

Link from Current Research section­> Smoothed Particle Hydrodynamics

­Periodic Boundary Condition Simulations

In this model a fluid is initially held in a square configuration along a sloped ramp with

open boundaries on both sides. At the the first time step the fluid is allow to flow outward due to

the force of gravity and begins to flow down the ramp. Once the fluid particles meet the boundary

edge on the right they cross over to the left side of the ramp. During the first few time steps the

fluid quickly moves to fill the void on the upper left hand side and crashes with slower moving

particles creating a significant splashing effect and the formation of a standing wave. Throughout

the simulation this standing wave begins to die out as the flow approaches a state of equilibrium.

Title: Exploring the method of smoothed particle hydrodynamics (SPH) and its application to

iceberg­capsize dynamics

Lynn Kaluzienski, 9/20/2015, University of Maine

Analytical solutions for problems in fluid dynamics are unavailable for most real world

flows. The method of Smoothed Particle Hydrodynamics (SPH) was initially developed for

astrophysical problems and has since been used to formulate approximate solutions for equations

in fluid dynamics, chiefly the Navier Stokes solution for a weakly compressible fluid. SPH takes

the innovative approach of replacing a fluid with an array of particles and solving the Navier

Stokes equation on a particle by particle basis. A smoothing function is applied to each individual

particle to determine the influence of its neighbors within a certain radius giving more weight to

nearby particles. SPH is naturally a mesh­free Lagrangian method, providing several benefits over

former grid­based techniques in capturing surface accelerations and removing the need of tracking

fluid boundaries. One difficulty with the SPH method is the need for a large quantity of particles to

achieve the same precision as a grid­based approach. However, recent improvements in

computational power such as the widespread use of graphic processing units (GPUs) have made

SPH implementation feasible and computationally inexpensive. Several open source codes, such as

DualSPHysics, make high resolution SPH simulations easily achievable on computers with

multiple GPU processing units. Depending on complexity, several hundred thousand particle

simulations can be achieved on the order of minutes to hours on a desktop computer. Larger­scale

models with millions to even billions of particles can be efficiently computed on supercomputers.

The University of Maine SECS Numerical Laboratory currently has SPH simulations running on

multiple GPUs. In addition, our collaboration with the Advanced Computing Group at Umaine will

allow us to run increasingly complex and higher resolution simulations on one of their

supercomputers in the near future.

Supporting Literature: Crespo et al 2015, Monaghan 2012

Link­> Supporting Animations

Each of these representations was exported from Paraview, a powerful visualization tool that stores

all output parameters (pressure, density, velocity, acceleration, vorticity, ID number) for each

particle at every time step.

­Dam­break Simulation

In this model a fluid is initially held in a block configuration. At the first time step the fluid is

allowed to flow out due to the force of gravity. As if flows outward it crashes into a rectangular

block and interacts with the boundary walls. The color of each fluid particle corresponds to its

velocity magnitude (m/s) at each time step.

­Initial Velocity Simulation

In this model two fluids with spherical and square configurations are given initial velocities. As

they collide with the square surface in the center they interact within a boxed boundary. The color

of each fluid particle corresponds to its velocity magnitude (m/s) at each time step.

­WaveMaker Simulation

In this model an oscillating piston creates wave within a fluid. The color of each fluid particle

corresponds to its ID number, thereby illustrating the effect of mixing throughout the simulation.

Link­> Introductory SPH Iceberg­capsize Simulations

­Wave Tank Experiment Simulation

In this model an oscillation piston creates waves within a 250 cm x 50 cm x 50 cm tank. A solid

block of 900 kg/m^3 density floats on one side of the tank and capsizes under the influence of the

standing waves.The color of each fluid particle corresponds to its velocity magnitude (m/s) at each

time step.

­Iceberg Closeup

In this view the motion of the particles at the boundary of the model iceberg are shown. The color

of each solid particle corresponds to its acceleration magnitude (m/s^2) at each time step.