philipphahn_ms_thesis_presentation.pdf

8/14/2019 PhilippHahn_MS_thesis_presentation.pdf

1/44

Philipp Hahn


2/44

Acknowledgements

Prof. Dan Negrut

Prof. Darryl Thelen

Prof. Michael Zinn

SBEL Colleagues:

Hammad Mazar, Toby Heyn, Manoj Kumar

2


3/44

Outline

Motivation

Lumped Mass Model

Model properties

Simulation results

Smoothed Particle Hydrodynamics (SPH)

SPH formulation for compressible fluids Serial and parallel Implementation

Numerical Experiments

Conclusion

3


4/44

Technical Background and Advantages of Meshless Methods

4


5/44


6/44


7/44

An Intermediate Step to Meshless Acoustics

7


8/44

Model Properties One-dimensional model consists of

N masses which are connected via

nonlinear springs

Masses represent the inertia of

certain gas volume

Spring forces replace pressure

forces

Equation of motion for each mass:

8


9/44


10/44

Properties & Implementation In the continuum limit, linearization leads to the following differential

equation:

The model does not draw on any linearization

Second order accuracy

Implementation & visualization in Matlab

10

Example with 9 Masses and Sinusoidal Excitation


11/44

Pressure can be calculated from spring forces at each point

Example with 300 mass points and sinusoidal excitation:

Simulation results

Linear Springs Nonlinear Springs

11


12/44

Simulation results

12

Soliton Waves

Stable soliton waves can be modeled

Propagation speed of soliton waves depends on their amplitude


13/44

Conclusion/Limitations Pro:

Speed of sound is modeled accurately

Known nonlinear effects can be reproduced Implementation is straightforward because of the simple model

Contra:

Stability of soliton waves depends on discretization

Due to the fixed connectivity, it is not a real meshless method

The transfer in two or three dimensional implementation is challenging

Move to a more promising method, called Smoothed particle

Hydrodynamics (SPH)

13


14/44

For Acoustic Simulations

14


15/44

SPH - The Basic Idea Mainly used in hydrodynamics and astronomy

Lagrangian particle method

Each particle carries field variables (density, internal energy, velocity,) A kernel-function approach defines the influence area of each particle

15

Field variables and their

derivatives can be approximated

with the following integrations:


16/44

SPH - The Basic Idea With the product rule of differentiation and the divergence theorem, field

function derivatives can also be expressed by:

The surface integral is zero if the kernel doesnt intersect domain boundaries

The Integration can be approximated by a summation

16


17/44


18/44

The Achilles heel of SPH (due to the kernel approximation)

Requirements on boundary formulations in acoustics: No boundary penetration

Accurate sound wave reflection

Accurate sound excitation (moving boundaries)

No disturbances

Boundary Formulations

18


19/44

Dynamic Boundary Particles

19

Pro:

Easy to implement

Contra:

Moving boundaries causedisturbances

Boundary penetration is

possible


20/44

Mirror Particles

20

Pro:

Theoretical exact boundary

treatment due to symmetry

Less disturbances Contra:

Boundary penetration is

possible:


21/44

Repulsive Forces

21

Pro:

No boundary penetration

Easy to implement

Contra: Large disturbances


22/44

Recall

Standard SPH neglects the surface integral in the formulation for field

function derivatives

This is the root of boundary problems

Newly developed Boundary

Treatment

22

The surface integral can be used efficiently if two assumptions are made:

The field function is constant on the boundary

The field function value is equal to or slightly higher than the particle

field function value (self interaction)


23/44

Newly developed Boundary

Treatment

23

Pro:

No boundary penetration

Computationally efficient

Contra:

disturbances

If boundaries are smooth, a generic

solution of the surface integral can be

used in simulations


24/44

SPH - Implementation

24

Structure and functionality

of a basic SPH

implementations:

Leap frog integration


25/44

2D Implementation in Matlab

25


26/44

2D Hydrodynamic Tests

26

SPH liquid particles are poured with a constant initial velocity

Boundary treatment through the new developed method

Water flow into a basin


27/44


27

A square of water is discretized by 7,225 SPH particles

Boundary treatment through dynamic boundary particles

The classic SPH test simulation: Dam break experiment


28/44

3D Implementation on the GPU Implementation in Matlab is only reasonable for one and two-

dimensional problems

10,000 particles (One time step 30s)

Solution: Leveraging the multiprocessor architecture of GPUs

The SPH algorithm is highly parallelizable

Nearest neighbor search in parallel (radixsort algorithm)

Derivatives (interaction parallel)

Integration (particle parallel)

Three dimensional Implementation using C++ and CUDA

CUDA API (programming tools for NVIDIA GPUs)

Simulations with up to 3.5 million particles are currently possible

Speed up of about 4,000 compared to Matlab

28


29/44


29

Parameters Number of particles:

250,000

Fluid properties:Water

Boundary formulation:Surface integrals

Time stepping:t=5.0e-5s

Length:T=1.0s

Computation time:2 hours

Droplet

simulation


30/44


30


82,000

Fluid properties:Water/Jelly



Length:T=1.5s


Different

Viscosities


31/44

Fluid-Structure Interaction

31

Boundary formulations typically require the following information:

Boundary position

Surface normal Can be describe analytically for simple shapes

Using spherical decomposition, arbitrary shaped boundaries can be

discretized by boundary particles.

position

Surface

normal

CAD geometry

Rigid bodymotion can be

determined using

fluid-structure

forces


32/44

Fluid-Structure Interaction

32


250,000

Fluid properties:Water



Length:T=4.5s


Water flow on

a trough


33/44

SPH in Acoustic Simulations Recall the advantages of SPH:

Whole flow process is solved; (speed of sound automatically adapts to

changing fluid properties)

Complex boundaries are possible; (spherical decomposition)

No linearizations ; (based on conservation laws)

Large deformations are unproblematic; (meshless Lagrangian method)

Highly parallelizable

What needs to be analyzed:

Sound propagation

Sound excitation and reflection

Scaling and accuracy

33


34/44

2D Sound propagationFDTD SPH

34

SPH models sound propagation accurately Speed of sound differs slightly


35/44

Effects of the Smoothing Length 1D Parameter study with different smoothing lengths

Velocity excitation from the left

Analytic solution is a traveling step function Level of the step can be related to the speed of sound

35


36/44

3D Sound Excitation/Reflection

36

3D sound excitation in a tube

Pressure wave excitation through the moving piston

Analytic solution is a traveling step function

Modeled with 270,000 SPH particles

Boundaries are first modeled with dynamic boundary particles and then

with a combination of mirror and dynamic boundary particles


37/44


37

Boundaries:

Pressure loss at

the edges:


38/44


Dynamic

Boundar

y

Particles

Mirror &Dynamic

Boundar

y

Particles

38


39/44

Computational Efficiency

39

3D experiment with concentric

sound propagation

six different resolutions are analyzed

The pressure at 1,000 positions after

a certain simulation time is compared

with results from FDTD


40/44

Contributions, Limitations, Future Work

40


41/44

Summary of contributions Analysis of meshless Lagrangian methods with focus on applicability in

acoustical engineering

Lumped mass model of one-dimensional nonlinear sound propagation

Implementation of SPH on the CPU using Matlab and on the GPU using

CUDA

Method to model fluid structure interaction through spherical

decomposition

Analysis of the impact of smoothing length on wave speed

Analysis of sound excitation due to moving boundaries

New, surface integral based, boundary formulation

Work-precision diagram for an acoustic SPH simulation

41


42/44

Limitations / Future Work Limitations

Deficient boundary formulations corrupt simulation results

Particle placement is critical and results are sensitive on particle disorder

Parameters have to be chosen correctly (experience is necessary)

Future Work

Improve boundary problematic (CSPH)

Nonlinear effects need to be analyzed

Fluid-structure interaction for shock waves Hydrodynamic simulations with fluid-structure interaction

42


43/44

Conclusion It is generally possible to use SPH in acoustic simulations

The scaling of the GPU implementation is good

Boundary formulations need to be improved

Simulating acoustic problems is not straightforward in SPH

Exact and noise free boundary enforcement

Particle placement

Right choice of parameters

Potential applications of SPH in Acoustics: aero-acoustic problems

complex and changing domain topologies

domains with multiple propagation media

domains with high temperature or density gradients

nonlinear acoustics and shock waves with fluid-structure interaction 43


44/44

philipphahn_ms_thesis_presentation.pdf

Documents