2000-02-08 Lecture 14: Flow visualisation Feature extraction - - PowerPoint PPT Presentation

Mats Nyl´ en February 8, 2000 Slide 1 of 13

2000-02-08

• Lecture 14:

– Flow visualisation – Feature extraction – Unsteady flow – Meteorological data VIS00

Mats Nyl´ en February 8, 2000 Slide 2 of 13

Flow visualization

Fluid flow contains at least

• density: ρ
• pressure: p
• flow velocity:

v I.e. two scalar fields and one vector field, these are connected by equations like the Navier-Stokes equation. Sometimes (like in PLOT3D files) flow momentum (≡ ρ v) is used instead of velocity. VIS00

Mats Nyl´ en February 8, 2000 Slide 3 of 13

The Navier-Stokes equation

The Navier-Stokes equation describes incompressible flow ∂ v ∂t + ( v · ∇) v = f − 1 ρ

• ∇p + ν∇2

v relating the flow velocity, v, to an external force, f, the pressure, p and the density ρ. ν is the (kinematic) viscosity. Sometimes the flow momentum, p = ρ v is used instead. VIS00

Mats Nyl´ en February 8, 2000 Slide 4 of 13

Flow around a pole

VIS00

Mats Nyl´ en February 8, 2000 Slide 5 of 13

Features

VIS00

Mats Nyl´ en February 8, 2000 Slide 6 of 13

Critical points

Critical points in a flow field v is points where the flow field posess special

• properties. Examples includes
• vorticies
• separation lines
• ridge and valley lines

Extracting and visualizing these features is called feature extraction. VIS00

Mats Nyl´ en February 8, 2000 Slide 7 of 13

Unsteady flows

Unsteady flows requires three additional considerations

• need to handle large data-sets,
• need to use time-dependant visualizations,
• needs time-dependant visualization techniques.

Each of these requirements represent a major step in comparison with steady flow visualization. VIS00

Mats Nyl´ en February 8, 2000 Slide 8 of 13

Advection for unsteady fields

We distinguish the following types of “lines”

• streamlines - field lines of

v,

• pathlines - trajectory of single particles,
• timelines - lines connecting particles released simultaneously,
• streaklines - line connecting particles released from the same location.

VIS00

Mats Nyl´ en February 8, 2000 Slide 9 of 13

Streamlines and pathlines

As before streamlines are solutions to d r dτ = v( r(τ), t) So each instant in time generates its own set of streamlines r(τ, t). Pathlines are solitions to the differential equations: d p dt = v( p(t), t) giving lines p(t). VIS00

Mats Nyl´ en February 8, 2000 Slide 10 of 13

Streaklines

Let us define p(t0, p0; t) as the pathline starting at p0 at t = t0, i.e. d p(t0, p0; t) dt = v( p(t0, p0; t), t) with initial condition:

• p(t0,

p0; t0) = p0 Then, a streakline is

• s(τ, t) =

p(t − τ, p0; t) VIS00

Mats Nyl´ en February 8, 2000 Slide 11 of 13

Meteorological data

Meteorological data may consist of

• Velocity field,
• Pressure,
• Temperature,
• Humidity (and water concentrations),

VIS00

Mats Nyl´ en February 8, 2000 Slide 12 of 13

Meteorological data

Since meteorology and climate modelling have Earth’s atmosphere (or parts

• f) computational domain certain features are particular
• the grid tends to be very assymetrical in the z-direction,
• various types of slices is used in the z-direction,
• U, V

and W is used for velocity, U is the east/west component of wind, V is the north/south component of wind and W is the vertical component of wind VIS00

Mats Nyl´ en February 8, 2000 Slide 13 of 13

Summary and outlook

This lecture was about flow-visualization. VIS00