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 f − 1 ∂� v ∇ p + ν ∇ 2 � v · � v = � � ∂t + ( � ∇ ) � v ρ v , to an external force, � relating the flow velocity, � 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 v ( � dτ = � 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 ( t 0 , � p 0 ; t ) as the pathline starting at � p 0 at t = t 0 , i.e. p ( t 0 , � p 0 ; t ) d� = � v ( � p ( t 0 , � p 0 ; t ) , t ) dt with initial condition: p ( t 0 , � p 0 ; t 0 ) = � � p 0 Then, a streakline is s ( τ, t ) = � p ( t − τ, � p 0 ; 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 of) 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