accuracy of pulsatile 2d flow in the lattice boltzmann bgk model
Download
Skip this Video
Download Presentation
Accuracy of Pulsatile 2D flow in the Lattice Boltzmann BGK model

Loading in 2 Seconds...

play fullscreen
1 / 20

Accuracy of Pulsatile 2D flow in the Lattice Boltzmann BGK model - PowerPoint PPT Presentation


  • 168 Views
  • Uploaded on

Accuracy of Pulsatile 2D flow in the Lattice Boltzmann BGK model. A. M. Artoli, A. G. Hoekstra and P. M. A. Sloot. Section Computational Science Institute Informatics Faculty of Science University of Amsterdam http://www.science.uva.nl/research/scs

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Accuracy of Pulsatile 2D flow in the Lattice Boltzmann BGK model' - Pat_Xavi


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
accuracy of pulsatile 2d flow in the lattice boltzmann bgk model

Accuracy of Pulsatile 2D flow in the Lattice Boltzmann BGK model

A. M. Artoli, A. G. Hoekstra and P. M. A. Sloot

Section Computational Science

Institute Informatics

Faculty of Science

University of Amsterdam

http://www.science.uva.nl/research/scs

Emails: [artoli, alfons, sloot]@science.uva.nl

overview
Overview
  • Motivation
  • The Lattice Boltzmann method
  • Benchmark
    • 2D Oscillatory Channel Flow
  • Simulation Results
  • Coclusions
motivation
Cardiovascular diseases are the main cause of human death.

Atherogenesis grows at locations of low and oscillating shear stress.

Shear stress can be computed easily and up to the same accuracy as the flow fields in LBM.

Motivation

Aorta with a bypass

the lattice boltzmann lbgk
The Lattice Boltzmann LBGK

The LBM is a first order finite difference discretization of the Boltzmann Equation

that describes the dynamics of continuous particle distribution function.

The velocity is descritized into a set of vectors ei

The inter-particle interactions are contained in the collision term W

The resulting Lattice Boltzmann involves two steps: streaming and Collision

simulations
Simulations
  • Flow is driven by a time dependent body force

P = A sin(w t) in the x-direction. A= initial Magnitude of P, w= angular frequency, t= simulation time .

  • Boundary conditions
    • inlet and outlet: Periodic boundaries.
    • Walls: bounce-Back
  • Parameters
    • a ranges from 1-15
    • t = 1
    • Grid size :
      • 2D : 10 x50 for a = 3.07 and 20 x100 for a=
      • 3D : 50 x 50 x 100
results
Results
  • 2D oscillatory Poiseuille flow
    • a =3.07
    • shown: Full-period analytic solutions (lines) and simulation results (points)
flow characteristics
Flow characteristics
  • There is a Phase lag between the pressure and the fluid motion.
  • At low a, steady Poiseuille flow is obtained.
  • At high a, we have the annular effect:
    • Profiles are flattened
    • The phase lag increases toward the center.
    • The shear stress is very low near the center and reasonably high at the walls.
conclusions
Conclusions
  • Obtaining accurate reproduction of 2D oscillatory flow is possible with incompressible LBGK.
  • Simulation results are more accurate if they are compared to analytic solutions at half time steps.
  • Pulsatile shear stress, directly computed from the distribution functions, yield accurate results.
boltzmann equation
Boltzmann Equation

Nonlinear integrodifferential equation in Kinetic theory of dilute monatomic gases.

Describes the temporal evolution of the one-particle distribution function in a gas of particles with binary collisions:

simplified be
Simplified BE

Equation is solvable near equilibrium

->Molecules are assumed Maxwellians -> gI(c) and not the energy.

Linearize the collision term and put fn = feqhn

-> Linearized BE

what is lost
What is lost?
  • Thermodynamic consistency between pressure and forcing
  • BGL?
    • Mass, radius and V ->0, N and r2 are finite => Perfect gas! -> Compressibility
  • But:
    • A gas that is not too rarefied (mfp->0) ~Fluid
    • NOT valid initially, near the boundaries and around shocks.
boundary conditions
Boundary conditions
  • Walls
    • Bounce-Back
    • Non slip
    • Curved
  • Inlet and Outlets
    • Velocity
    • Pressure
    • No flux
enhancing the lbgk
Enhancing the LBGK
  • Incompressibility
    • D2Q9 ->D2Q9i-> D2Q9ii, ...
  • Stability
    • subgrid models
  • Thermodynamic consistency
    • Non-ideal gas models
conclusions 3d
Conclusions, 3D
  • LBGK with the simple bounce back produces an error > 12% for steady and unsteady flows.
  • Enhanced LBGK or LBE model reduces the error .
  • Curved boundary conditions should be used.
ad