Flow Visualisation  Background. CITS4241 Visualisation Lectures 20 and 21


 Linette Berry
 5 years ago
 Views:
Transcription
1 CITS4241 Visualisation Lectures 20 and 21 Flow Visualisation Flow visualisation is important in both science and engineering From a "theoretical" study of o turbulence or o a fusion reactor plasma, to the "practical" design of o airplane wings or o jet nozzles. The main challenge Find ways to represent and visualize (very) large, multidimensional, multivariate data. Do this accurately, and Be computationally tractable 2 Flow data in an Ndimensional space can be univariate (Ndimensional scalar fields), Nvariate (Ndimensional vector fields) or even N 2 variate (Ndimensional second order tensor fields) Visualisation of results from a numerical flow simulation, Often a Computational Fluid Dynamics (CFD) calculation CFD studies the flow of fluids in and around complex structures Large amounts of supercomputer time are often required to derive the scalar and vector data in the flow field Flow visualisation will typically consist of 3 phases Grid generation, where the grid may be o rectilinear, o curvilinear, o unstructured, or a o hybrid  structured and unstructured. o Typically the calculation over grid points Flow calculation solution of a system of NavierStokes equations that simulate the flow conditions Computationally intensive  generates data for several quantities typically, momentum, density, energy and velocity Equations may be solved for time steps
2 Visualisation Render results obtained from phases 1 and 2 into a form easily understood by humans We are already familiar with many of the issues associated with visualisation Interactive visualisation is not possible because of the size of the problem Problem Size Example Problem and solution data requirements for some numerical aerodynamic simulations Clipped Delta Wing Grid Points 250,000 Grid File 4 MB Solution File (per time step) 9MB Time Steps 5,000 X 3 cycles Total per Simulation 135GB Descending Delta Wing 900,000 16MB 36MB 90,000 3,240GB SOFIA Airplane 3.2E+06 53MB 119MB 10,000 1,190GB 5 6 In interactive visualisation, it is ideal to store all time steps of the data in physical memory, clearly the results from 3D unsteady flow data are too large (from the table earlier) to enable interactive visualisation Even storing a few time steps becomes prohibitive! Postvisualisation is usually performed, I.e. Data are saved first, and visualisation is carried out later Postvisualisation Several approaches: 1. Load into memory as many time steps of the saved data as possible, For small dataset o this approach is attractive, and o interactive visualisation is possible For large dataset o only an unacceptably small number of time steps can be loaded 2. Subsamples the saved data at lower grid resolution so that more time steps can fit in memory Not favoured approach because it is expensive to subsample, and resolution of the flow is poor Important flow features, eg vortices, can be missed 7 8 2
3 Postvisualisation (cont.) Several approaches: 3. Load into memory every step of the saved data without subsampling This requires that the system has enough memory to store at least a few time steps of the data This approach of visualising flow data at instants in time is sometimes referred to as instantaneous flow visualisation Visualisation mappings The process of visualisation involves Data processing, which can involve o Interpolation o Filtering o Deriving fitted functions o Visualisation mapping Translation of data into a suitable (iconic) representation (which involves deciding which features in the data are meaningful) o Rendering The generation of the final image that conveys the information to the user 9 10 Icons Hesselink and Delmarcelle [4] define three types of elementary vector icons used in flow visualisation. These are point icons, line icons, and surface icons 1. Point icons: When drawing arrows at selected points in the flow field, point icons are often superimposed in the field to denote the tails of the arrows Point icons are also used to highlight important features, such as critical points, of vector fields. Critical points in vector fields can be o points in the flow where the flow magnitude vanishes, or o points in the flow where the slope of the streamline ( see later) is locally undefined (e.g. approaching infinity), or o points where streamlines cross note that streamlines never cross each other except at critical points. 11 Icons (cont.) An example of point icon Note the small dots displayed at one end of each line segment 12 3
4 Icons (cont.) 2. Line icons Line icons are lines/curves drawn to show the directions and magnitudes of the flow vectors Line icons are more efficient in the sense that they provide a continuous representation of the data, thus avoiding mental interpolation of point icons. Common line icons used are: o Particle traces Particle traces are trajectories traversed by fluid elements over time. A collection of particle traces therefore gives a sense of the complete time evolution of the flow o Streaklines The streakline of the point x 0 at time t 0 is formally defined as the locus at time t 0 of all the fluid elements that have previously passed through x 0 Streaklines therefore emphasize the past history of the flow Icons (cont.) o Streamlines Streamlines at time t 0 are curves that are everywhere tangential to the vector field v(x, t 0 ). A collection of such streamlines therefore provide an instantaneous picture of the flow at time t 0 In general, particle traces, streaklines, and streamlines are distinct from each other, but these 3 families of trajectories coincide in steady flows Icons (cont.) An example of Streamlines Some important features that were 'hidden before are now visible Particle traces are clearly better here! Streamribbons We will look at two more line icons here: streamribbons and streamtubes Streamribbons are narrow surfaces between two adjacent streamlines They are built from a front with only two particles They reflect flow divergence through changing width, and Vortices are shown in the degree of twist in the ribbon
5 Streamtubes An easy way to generate streamtubes is to sweep an N sided polygon along each streamline. The rotation of the edges found in the tube represent streamwise vorticity and the crosssection encodes cross flow divergence. Streamtubes (cont.) another example The streamtube has hexagonal crossseciton A streamline and streamribbon are added for comparison and stream ribbons or stream tubes are arguably better still. Streampolygon (crosssection of streamtube) Rotation of edges vorticity Area of polygon divergence Surface Icons Streamsurfaces This is the third type of elementary icons Generation of streamsurfaces Start with userdefined rake Generate streamlines from rake particles Construct a polygonal mesh to join adjacent streamlines Difficulties Field divergence can cause streamlines to o separate image interpretation difficulties or even o cross over not physically possible!! Surface Icons Streamsurfaces (cont.) Streamsurfaces provide additional information Any point on the surface is a tangent to the flow No particle can pass through the surface In a fluid dynamic (or similar) application, represent constant mass flux o Could view them as contours for the flow density Streamsurfaces are better than vector glyphs They don't require interpolation (by viewer) between icons
6 Streamsurfaces An Example Streamsurfaces work well in certain cases Extra streamlines added here Note the divergence Original particle front is a line segment of 6 particles, Surface is generated by polygonal tiling between pairs of adjacent streamlines Tensor Mappings Many physical quantities in fluid flows are tensors Their visualisation can provide significant insight into behaviours in fluids. Next level of difficulty! o (above scalar and vector data) Expected that there are fewer mapping idioms developed. Tensor data tends to be 2 or 3 times more multivariate o Recall vector data is Nvariate and tensor data is N 2 variate) than vector fields more complex to visualise! Tensor Mappings (cont.) One of the more natural representations of tensor data is as a set of eigenvectors. This may appear easy one can associate a simple icon with a vector, but this representation is not intuitive when dealing with sets of vectors. Humans are not well versed in the visualisation of tensor data Abstraction is necessary to give a meaningful image Symmetric tensor data We will restrict ourselves to R 3 space (tensors can be represented as a matrix), and Symmetric tensors of the form U = [U ik ] and U ik =U ki. I.e. U is a 3x3 symmetric matrix. Equivalent to three orthogonal vector fields U has three (3) real eigenvalues r i and three (3) real, orthogonal eigenvectors e i ( i=1,2,3 ) for each point x in space Construct three orthogonal vectors: v i = r i e i Adopt the convention: r 1 > r 2 > r 3 This results in v 1, v 2, v 3 being the major, medium and minor eigenvectors respectively
7 Symmetric tensor data Point icons in tensor mapping? Visualising U is equivalent to simultaneously visualising three (3) vector fields v i, Each has o amplitude (r i ) and o direction (e i ). Clutter is an even greater problem with tensor data Density of the icon placement must be even less than usual Requiring significant mental interpolation between icons to discern the structure of the tensor field Hyperstreamlines Line icons improve ability to visualise a continuous tensor field, just as it did for vector mappings. One could Use a streamline representation for one of the vector fields v i This will emphasise the continuity of that field but not highlight the correlations that exist between the three eigenvector fields The icon we need must represent all tensor information along the trajectory, or encode the continuous distribution of ellipsoids (an equivalent viewpoint) Generalise vector streamlines tensor hyperstreamlines Hyperstreamlines (cont.) Generation Streamlines are constructed by creating a streamline through one of the three eigenvector fields v i, and then sweeping a geometric primitive along the streamline (I.e. stretching the transverse plane under the action of the other 2 eigenvector fields) Typically, an ellipse is often used as the geometric primitive o The major and minor axes of an ellipse can represent the other 2 fields o Sweep this ellipse along the first vector field Use polygons to join ellipses
8 Hyperstreamlines Hyperstreamlines Object with 2 compressive loadings 'Cones' sweep along one strain direction (streamline for one eigenvector) Crosssection through cone ellipse representing 2 other strain directions Object with 2 compressive loadings 'Cones' sweep along one strain direction (streamline for one one eigenvector) Lower blue regions are streamribbons for the 'other' strains  they are everywhere to the principal strain References 1. Thierry Delmarcelle and Lambertus Hesselink, "Visualizing SecondOrder Tensor Fields and Matrix Data", Proc. IEEE Conference on Visualization,1992, pages Article available at IEEE Xplore. 2. Thierry Delmarcelle and Lambertus Hesselink, "Visualizing SecondOrder Tensor Fields with Hyperstreamlines", IEEE Trans. on Computer Graphics and Applications, vol. 13, No. 4, 1993, pages Article available at IEEE Xplore. 3. Thierry Delmarcelle and Lambertus Hesselink, "A Unified Framework for Flow Visualization", in Computer Visualization: Graphics Techniques for Scientific and Engineering Analysis (R. Gallagher, editor), chapter 5, CRC Press, L. Hesselink and T. Delmarcelle, Visualization of Vector and Tensor Data Sets, in Scientific Visualization Advances and Challenges, edited by Rosenblum et al., Academic Press, David A. Lane, "Scientific Visualization of Large Scale Unsteady Fluid Flow" in Scientific Visualization Surveys, Methodologies and Techniques, IEEE Computer Society Press, 1996, pages Article available at 6. F. J. Post, T. van Walsum, and F. H. Post. "Iconic techniques for feature visualization". In Proceedings Visualization '95, pages , Will Schroeder, Ken Martin, and Bill Lorensen, "The Visualization Toolkit  An ObjectOriented Approach to 3D Graphics", 2nd Ed., PrenticeHall, 1998, Section 6.5, pages ; Section 9.2, pages , pages
Vector Visualization. CSC 7443: Scientific Information Visualization
Vector Visualization Vector data A vector is an object with direction and length v = (v x,v y,v z ) A vector field is a field which associates a vector with each point in space The vector data is 3D representation
More informationLecture overview. Visualisatie BMT. Vector algorithms. Vector algorithms. Time animation. Time animation
Visualisatie BMT Lecture overview Vector algorithms Tensor algorithms Modeling algorithms Algorithms  2 Arjan Kok a.j.f.kok@tue.nl 1 2 Vector algorithms Vector 2 or 3 dimensional representation of direction
More informationFlow Visualisation 1
Flow Visualisation Visualisation Lecture 13 Institute for Perception, Action & Behaviour School of Informatics Flow Visualisation 1 Flow Visualisation... so far Vector Field Visualisation vector fields
More informationVector Field Visualisation
Vector Field Visualisation Computer Animation and Visualization Lecture 14 Institute for Perception, Action & Behaviour School of Informatics Visualising Vectors Examples of vector data: meteorological
More informationChapter 6 Visualization Techniques for Vector Fields
Chapter 6 Visualization Techniques for Vector Fields 6.1 Introduction 6.2 Vector Glyphs 6.3 Particle Advection 6.4 Streamlines 6.5 Line Integral Convolution 6.6 Vector Topology 6.7 References 2006 Burkhard
More information8. Tensor Field Visualization
8. Tensor Field Visualization Tensor: extension of concept of scalar and vector Tensor data for a tensor of level k is given by t i1,i2,,ik (x 1,,x n ) Secondorder tensor often represented by matrix Examples:
More informationVector Visualisation 1. global view
Vector Field Visualisation : global view Visualisation Lecture 12 Institute for Perception, Action & Behaviour School of Informatics Vector Visualisation 1 Vector Field Visualisation : local & global Vector
More informationData Visualization. Fall 2017
Data Visualization Fall 2017 Vector Fields Vector field v: D R n D is typically 2D planar surface or 2D surface embedded in 3D n = 2 fields tangent to 2D surface n = 3 volumetric fields When visualizing
More informationFlow Visualization with Integral Surfaces
Flow Visualization with Integral Surfaces Visual and Interactive Computing Group Department of Computer Science Swansea University R.S.Laramee@swansea.ac.uk 1 1 Overview Flow Visualization with Integral
More information3D vector fields. Contents. Introduction 3D vector field topology Representation of particle lines. 3D LIC Combining different techniques
3D vector fields Scientific Visualization (Part 9) PD Dr.Ing. Peter Hastreiter Contents Introduction 3D vector field topology Representation of particle lines Path lines Ribbons Balls Tubes Stream tetrahedra
More informationVector Visualization
Vector Visualization Vector Visulization Divergence and Vorticity Vector Glyphs Vector Color Coding Displacement Plots Stream Objects TextureBased Vector Visualization Simplified Representation of Vector
More informationA Broad Overview of Scientific Visualization with a Focus on Geophysical Turbulence Simulation Data (SciVis
A Broad Overview of Scientific Visualization with a Focus on Geophysical Turbulence Simulation Data (SciVis 101 for Turbulence Researchers) John Clyne clyne@ucar.edu Examples: Medicine Examples: Biology
More informationUsing Integral Surfaces to Visualize CFD Data
Using Integral Surfaces to Visualize CFD Data Tony Mcloughlin, Matthew Edmunds,, Mark W. Jones, Guoning Chen, Eugene Zhang 1 1 Overview Flow Visualization with Integral Surfaces: Introduction to flow visualization
More informationScaling the Topology of Symmetric, SecondOrder Planar Tensor Fields
Scaling the Topology of Symmetric, SecondOrder Planar Tensor Fields Xavier Tricoche, Gerik Scheuermann, and Hans Hagen University of Kaiserslautern, P.O. Box 3049, 67653 Kaiserslautern, Germany Email:
More informationPart I: Theoretical Background and IntegrationBased Methods
Large Vector Field Visualization: Theory and Practice Part I: Theoretical Background and IntegrationBased Methods Christoph Garth Overview Foundations TimeVarying Vector Fields Numerical Integration
More informationmjb March 9, 2015 Chuck Evans
Vector Visualization What is a Vector Visualization Problem? A vector has direction and magnitude. Typically science and engineering problems that work this way are those involving fluid flow through a
More informationCIS 467/60201: Data Visualization
CIS 467/60201: Data Visualization Vector Field Visualization Dr. David Koop Fields Tables Networks & Trees Fields Geometry Clusters, Sets, Lists Items Items (nodes) Grids Items Items Attributes Links
More informationAn Introduction to Flow Visualization (1) Christoph Garth
An Introduction to Flow Visualization (1) Christoph Garth cgarth@ucdavis.edu Motivation What will I be talking about? Classical: Physical experiments to understand flow. 2 Motivation What will I be talking
More informationVolume Illumination & Vector Field Visualisation
Volume Illumination & Vector Field Visualisation Visualisation Lecture 11 Institute for Perception, Action & Behaviour School of Informatics Volume Illumination & Vector Vis. 1 Previously : Volume Rendering
More informationVector Visualization Chap. 6 March 7, 2013 March 26, Jie Zhang Copyright
ector isualization Chap. 6 March 7, 2013 March 26, 2013 Jie Zhang Copyright CDS 301 Spring, 2013 Outline 6.1. Divergence and orticity 6.2. ector Glyphs 6.3. ector Color Coding 6.4. Displacement Plots (skip)
More informationLecture 1.1 Introduction to Fluid Dynamics
Lecture 1.1 Introduction to Fluid Dynamics 1 Introduction A thorough study of the laws of fluid mechanics is necessary to understand the fluid motion within the turbomachinery components. In this introductory
More informationChapter 1  Basic Equations
2.20 Marine Hydrodynamics, Fall 2017 Lecture 2 Copyright c 2017 MIT  Department of Mechanical Engineering, All rights reserved. 2.20 Marine Hydrodynamics Lecture 2 Chapter 1  Basic Equations 1.1 Description
More informationIntroduction to Computational Fluid Dynamics Mech 122 D. Fabris, K. Lynch, D. Rich
Introduction to Computational Fluid Dynamics Mech 122 D. Fabris, K. Lynch, D. Rich 1 Computational Fluid dynamics Computational fluid dynamics (CFD) is the analysis of systems involving fluid flow, heat
More informationVector Visualization
Vector Visualization 51 Vector Algorithms Vector data is a threedimensional representation of direction and magnitude. Vector data often results from the study of fluid flow, or when examining derivatives,
More information11/1/13. Visualization. Scientific Visualization. Types of Data. Height Field. Contour Curves. Meshes
CSCI 420 Computer Graphics Lecture 26 Visualization Height Fields and Contours Scalar Fields Volume Rendering Vector Fields [Angel Ch. 2.11] Jernej Barbic University of Southern California Scientific Visualization
More informationVisualization. CSCI 420 Computer Graphics Lecture 26
CSCI 420 Computer Graphics Lecture 26 Visualization Height Fields and Contours Scalar Fields Volume Rendering Vector Fields [Angel Ch. 11] Jernej Barbic University of Southern California 1 Scientific Visualization
More informationVector Field Visualization: Introduction
Vector Field Visualization: Introduction What is a Vector Field? Why It is Important? Vector Fields in Engineering and Science Automotive design [Chen et al. TVCG07,TVCG08] Weather study [Bhatia and Chen
More informationFundamental Algorithms
Fundamental Algorithms Fundamental Algorithms 31 Overview This chapter introduces some basic techniques for visualizing different types of scientific data sets. We will categorize visualization methods
More informationLecture overview. Visualisatie BMT. Goal. Summary (1) Summary (3) Summary (2) Goal Summary Study material
Visualisatie BMT Introduction, visualization, visualization pipeline Arjan Kok a.j.f.kok@tue.nl Lecture overview Goal Summary Study material What is visualization Examples Visualization pipeline 1 2 Goal
More informationFLUID MECHANICS TESTS
FLUID MECHANICS TESTS Attention: there might be more correct answers to the questions. Chapter 1: Kinematics and the continuity equation T.2.1.1A flow is steady if a, the velocity direction of a fluid
More informationLecture overview. Visualisatie BMT. Fundamental algorithms. Visualization pipeline. Structural classification  1. Structural classification  2
Visualisatie BMT Fundamental algorithms Arjan Kok a.j.f.kok@tue.nl Lecture overview Classification of algorithms Scalar algorithms Vector algorithms Tensor algorithms Modeling algorithms 1 2 Visualization
More informationData Visualization (CIS/DSC 468)
Data Visualization (CIS/DSC 468) Vector Visualization Dr. David Koop Visualizing Volume (3D) Data 2D visualization slice images (or multiplanar reformating MPR) Indirect 3D visualization isosurfaces (or
More informationPlanes Intersecting Cones: Static Hypertext Version
Page 1 of 12 Planes Intersecting Cones: Static Hypertext Version On this page, we develop some of the details of the planeslicingcone picture discussed in the introduction. The relationship between the
More informationSystem Design for Visualizing Scientific Computations
25 Chapter 2 System Design for Visualizing Scientific Computations In Section 1.1 we defined five broad goals for scientific visualization. Specifically, we seek visualization techniques that 1. Can be
More informationHierarchical Streamarrows for the Visualization of Dynamical Systems
Hierarchical Streamarrows for the Visualization of Dynamical Systems Helwig Löffelmann Lukas Mroz Eduard Gröller Institute of Computer Graphics, Vienna University of Technology Abstract. Streamarrows are
More informationDISCONTINUOUS FINITE ELEMENT VISUALIZATION
1 1 8th International Symposium on Flow Visualisation (1998) DISCONTINUOUS FINITE ELEMENT VISUALIZATION A. O. Leone P. Marzano E. Gobbetti R. Scateni S. Pedinotti Keywords: visualization, highorder finite
More informationScientific Visualization Example exam questions with commented answers
Scientific Visualization Example exam questions with commented answers The theoretical part of this course is evaluated by means of a multiple choice exam. The questions cover the material mentioned during
More informationScientific Visualization. CSC 7443: Scientific Information Visualization
Scientific Visualization Scientific Datasets Gaining insight into scientific data by representing the data by computer graphics Scientific data sources Computation Real material simulation/modeling (e.g.,
More informationVisualization Computer Graphics I Lecture 20
15462 Computer Graphics I Lecture 20 Visualization Height Fields and Contours Scalar Fields Volume Rendering Vector Fields [Angel Ch. 12] November 20, 2003 Doug James Carnegie Mellon University http://www.cs.cmu.edu/~djames/15462/fall03
More informationFLOWING FLUIDS AND PRESSURE VARIATION
Chapter 4 Pressure differences are (often) the forces that move fluids FLOWING FLUIDS AND PRESSURE VARIATION Fluid Mechanics, Spring Term 2011 e.g., pressure is low at the center of a hurricane. For your
More informationChapter 8 Visualization and Optimization
Chapter 8 Visualization and Optimization Recommended reference books: [1] Edited by R. S. Gallagher: Computer Visualization, Graphics Techniques for Scientific and Engineering Analysis by CRC, 1994 [2]
More informationVector Field Visualization: Introduction
Vector Field Visualization: Introduction What is a Vector Field? A simple 2D steady vector field A vector valued function that assigns a vector (with direction and magnitude) to any given point. It typically
More informationMAE 3130: Fluid Mechanics Lecture 5: Fluid Kinematics Spring Dr. Jason Roney Mechanical and Aerospace Engineering
MAE 3130: Fluid Mechanics Lecture 5: Fluid Kinematics Spring 2003 Dr. Jason Roney Mechanical and Aerospace Engineering Outline Introduction Velocity Field Acceleration Field Control Volume and System Representation
More informationMESHLESS SOLUTION OF INCOMPRESSIBLE FLOW OVER BACKWARDFACING STEP
Vol. 12, Issue 1/2016, 6368 DOI: 10.1515/cee20160009 MESHLESS SOLUTION OF INCOMPRESSIBLE FLOW OVER BACKWARDFACING STEP Juraj MUŽÍK 1,* 1 Department of Geotechnics, Faculty of Civil Engineering, University
More informationVisualization Computer Graphics I Lecture 20
15462 Computer Graphics I Lecture 20 Visualization Height Fields and Contours Scalar Fields Volume Rendering Vector Fields [Angel Ch. 12] April 15, 2003 Frank Pfenning Carnegie Mellon University http://www.cs.cmu.edu/~fp/courses/graphics/
More informationVisualization, Lecture #2d. Part 3 (of 3)
Visualization, Lecture #2d Flow visualization Flow visualization, Part 3 (of 3) Retrospect: Lecture #2c Flow Visualization, Part 2: FlowVis with arrows numerical integration Eulerintegration RungeKuttaintegration
More informationFlow Visualization: The StateoftheArt
Flow Visualization: The StateoftheArt The Visual and Interactive Computing Group Computer Science Department Swansea University Swansea, Wales, UK 1 Overview Introduction to Flow Visualization (FlowViz)
More informationCourse Review. Computer Animation and Visualisation. Taku Komura
Course Review Computer Animation and Visualisation Taku Komura Characters include Human models Virtual characters Animal models Representation of postures The body has a hierarchical structure Many types
More informationTexture Advection. Ronald Peikert SciVis Texture Advection 61
Texture Advection Ronald Peikert SciVis 2007  Texture Advection 61 Texture advection Motivation: dense visualization of vector fields, no seed points needed. Methods for static fields: LIC  Line integral
More information1 Mathematical Concepts
1 Mathematical Concepts Mathematics is the language of geophysical fluid dynamics. Thus, in order to interpret and communicate the motions of the atmosphere and oceans. While a thorough discussion of the
More informationProf. Fanny Ficuciello Robotics for Bioengineering Visual Servoing
Visual servoing vision allows a robotic system to obtain geometrical and qualitative information on the surrounding environment high level control motion planning (lookandmove visual grasping) low level
More informationOver Two Decades of IntegrationBased, Geometric Vector Field. Visualization
Over Two Decades of IntegrationBased, Geometric Vector Field Visualization Tony McLoughlin1, 1, Ronald Peikert2, Frits H. Post3, and Min Chen1 1 The Visual and Interactive Computing Group Computer Science
More informationHeight Fields and Contours Scalar Fields Volume Rendering Vector Fields [Angel Ch. 12] April 23, 2002 Frank Pfenning Carnegie Mellon University
15462 Computer Graphics I Lecture 21 Visualization Height Fields and Contours Scalar Fields Volume Rendering Vector Fields [Angel Ch. 12] April 23, 2002 Frank Pfenning Carnegie Mellon University http://www.cs.cmu.edu/~fp/courses/graphics/
More informationIntroduction to CFX. Workshop 2. Transonic Flow Over a NACA 0012 Airfoil. WS21. ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.
Workshop 2 Transonic Flow Over a NACA 0012 Airfoil. Introduction to CFX WS21 Goals The purpose of this tutorial is to introduce the user to modelling flow in high speed external aerodynamic applications.
More informationACGV 2008, Lecture 1 Tuesday January 22, 2008
Advanced Computer Graphics and Visualization Spring 2008 Ch 1: Introduction Ch 4: The Visualization Pipeline Ch 5: Basic Data Representation Organization, Spring 2008 Stefan Seipel Filip Malmberg Mats
More informationIntroduction to C omputational F luid Dynamics. D. Murrin
Introduction to C omputational F luid Dynamics D. Murrin Computational fluid dynamics (CFD) is the science of predicting fluid flow, heat transfer, mass transfer, chemical reactions, and related phenomena
More informationCP SC 8810 Data Visualization. Joshua Levine
CP SC 8810 Data Visualization Joshua Levine levinej@clemson.edu Lecture 05 Visual Encoding Sept. 9, 2014 Agenda Programming Lab 01 Questions? Continuing from Lec04 Attribute Types no implicit ordering
More informationData Representation in Visualisation
Data Representation in Visualisation Visualisation Lecture 4 Taku Komura Institute for Perception, Action & Behaviour School of Informatics Taku Komura Data Representation 1 Data Representation We have
More informationChapter 2: From Graphics to Visualization
Exercises for Chapter 2: From Graphics to Visualization 1 EXERCISE 1 Consider the simple visualization example of plotting a graph of a twovariable scalar function z = f (x, y), which is discussed in
More information1. Interpreting the Results: Visualization 1
1. Interpreting the Results: Visualization 1 visual/graphical/optical representation of large sets of data: data from experiments or measurements: satellite images, tomography in medicine, microsopy,...
More informationScalar Visualization
Scalar Visualization 51 Motivation Visualizing scalar data is frequently encountered in science, engineering, and medicine, but also in daily life. Recalling from earlier, scalar datasets, or scalar fields,
More informationFlow Structures Extracted from Visualization Images: Vector Fields and Topology
Flow Structures Extracted from Visualization Images: Vector Fields and Topology Tianshu Liu Department of Mechanical & Aerospace Engineering Western Michigan University, Kalamazoo, MI 49008, USA We live
More informationScalar Visualization
Scalar Visualization Visualizing scalar data Popular scalar visualization techniques Color mapping Contouring Height plots outline Recap of Chap 4: Visualization Pipeline 1. Data Importing 2. Data Filtering
More informationSurface Representations of Two and ThreeDimensional. Fluid Flow Topology
Surface Representations of Two and ThreeDimensional Fluid Flow Topology J. L. Helman Lambertus Hesselink Department of Applied Physics Departments of Aeronautics/Astronautics and Electrical Engineering
More informationVisualisation of uncertainty. KaiMikael JääAro
Visualisation of uncertainty KaiMikael JääAro Why is this important? Visualising uncertainty Means and Methods Scalar data Vector data Volume data Generic methods Let us talk about the weather A weather
More informationVisualization. Images are used to aid in understanding of data. Height Fields and Contours Scalar Fields Volume Rendering Vector Fields [chapter 26]
Visualization Images are used to aid in understanding of data Height Fields and Contours Scalar Fields Volume Rendering Vector Fields [chapter 26] Tumor SCI, Utah Scientific Visualization Visualize large
More informationNUMERICAL 3D TRANSONIC FLOW SIMULATION OVER A WING
Review of the Air Force Academy No.3 (35)/2017 NUMERICAL 3D TRANSONIC FLOW SIMULATION OVER A WING Cvetelina VELKOVA Department of Technical Mechanics, Naval Academy Nikola Vaptsarov,Varna, Bulgaria (cvetelina.velkova1985@gmail.com)
More informationVisualization with ParaView
Visualization with Before we begin Make sure you have 3.10.1 installed so you can follow along in the lab section http://paraview.org/paraview/resources/software.html http://www.paraview.org/ Background
More informationShape optimisation using breakthrough technologies
Shape optimisation using breakthrough technologies Compiled by Mike Slack Ansys Technical Services 2010 ANSYS, Inc. All rights reserved. 1 ANSYS, Inc. Proprietary Introduction Shape optimisation technologies
More informationSeparation in threedimensional steady flows. Part 2 : DETACHMENT AND ATTACHMENT SEPARATION LINES DETACHMENT AND ATTACHMENT SEPARATION SURFACES
Separation in threedimensional steady flows Part 2 : DETACHMENT AND ATTACHMENT SEPARATION LINES DETACHMENT AND ATTACHMENT SEPARATION SURFACES Separation lines or separatrices A separation line is a skin
More informationInteractive Visualization of Mixed Scalar and Vector Fiel
Interactive Visualization of Mixed Scalar and Vector Fiel Lichan Hong, Xiaoyang Mao: and Arie Kaufman Department of Computer Science State University of New York at Stony Brook Stony Brook, NY 117944400
More informationFlow Visualization with Integral Objects. Visualization, Lecture #2d. Streamribbons, Streamsurfaces, etc. Flow visualization, Part 3 (of 3)
Visualization, Lecture #2d Flow visualization, Part 3 (of 3) Flow Visualization with Integral Objects Streamribbons, Streamsurfaces, etc. Retrospect: Lecture #2c Flow Visualization, Part 2: FlowVis with
More informationStream Hulls: A 3D Visualization Technique for Chaotic Dynamical Systems
Stream Hulls: A 3D Visualization Technique for Chaotic Dynamical Systems Kenny Gruchalla Elizabeth Bradley Department of Computer Science, University of Colorado at Boulder, Boulder, Colorado 80309 gruchall@cs.colorado.edu
More informationcomputational Fluid Dynamics  Prof. V. Esfahanian
Three boards categories: Experimental Theoretical Computational Crucial to know all three: Each has their advantages and disadvantages. Require validation and verification. School of Mechanical Engineering
More informationANSYS AIM Tutorial Turbulent Flow Over a Backward Facing Step
ANSYS AIM Tutorial Turbulent Flow Over a Backward Facing Step Author(s): Sebastian Vecchi, ANSYS Created using ANSYS AIM 18.1 Problem Specification PreAnalysis & Start Up Governing Equation StartUp Geometry
More informationCurve and Surface Basics
Curve and Surface Basics Implicit and parametric forms Power basis form Bezier curves Rational Bezier Curves Tensor Product Surfaces ME525x NURBS Curve and Surface Modeling Page 1 Implicit and Parametric
More informationChapter 1  Basic Equations
2.20  Marine Hydrodynamics, Sring 2005 Lecture 2 2.20 Marine Hydrodynamics Lecture 2 Chater 1  Basic Equations 1.1 Descrition of a Flow To define a flow we use either the Lagrangian descrition or the
More informationLecture Topic Projects 1 Intro, schedule, and logistics 2 Applications of visual analytics, basic tasks, data types 3 Introduction to D3, basic vis
Lecture Topic Projects 1 Intro, schedule, and logistics 2 Applications of visual analytics, basic tasks, data types 3 Introduction to D3, basic vis techniques for nonspatial data Project #1 out 4 Data
More informationThree Dimensional Numerical Simulation of Turbulent Flow Over Spillways
Three Dimensional Numerical Simulation of Turbulent Flow Over Spillways Latif Bouhadji ASLAQFlow Inc., Sidney, British Columbia, Canada Email: lbouhadji@aslenv.com ABSTRACT Turbulent flows over a spillway
More informationds dt ds 1 dt 1 dt v v v dt ds and the normal vector is given by N
Normal Vectors and Curvature In the last section, we stated that reparameterization by arc length would help us analyze the twisting and turning of a curve. In this section, we ll see precisely how to
More informationDaniel Keefe. Computer Science Department: Brown University. April 17, 2000
Artistic Metaphors for Interactive Visualization of MultiValued 3D Data Research Comp. Proposal Daniel Keefe Computer Science Department: Brown University April 17, 2000 1 Introduction and Motivation
More informationChapter 3: Kinematics Locomotion. Ross Hatton and Howie Choset
Chapter 3: Kinematics Locomotion Ross Hatton and Howie Choset 1 (Fully/Under)Actuated Fully Actuated Control all of the DOFs of the system Controlling the joint angles completely specifies the configuration
More informationUse of numerical flow simulations (CFD) for optimising heat exchangers
www.guentner.eu Technical article from 03.04.2017 Author Dr. Andreas Zürner Research Güntner GmbH & Co. KG Use of numerical flow simulations (CFD) for optimising heat exchangers Numerical flow simulations
More informationThe Development of a NavierStokes Flow Solver with Preconditioning Method on Unstructured Grids
Proceedings of the International MultiConference of Engineers and Computer Scientists 213 Vol II, IMECS 213, March 1315, 213, Hong Kong The Development of a NavierStokes Flow Solver with Preconditioning
More informationComputer Graphics I Lecture 11
15462 Computer Graphics I Lecture 11 Midterm Review Assignment 3 Movie Midterm Review Midterm Preview February 26, 2002 Frank Pfenning Carnegie Mellon University http://www.cs.cmu.edu/~fp/courses/graphics/
More informationTutorial 2: Particles convected with the flow along a curved pipe.
Tutorial 2: Particles convected with the flow along a curved pipe. Part 1: Creating an elbow In part 1 of this tutorial, you will create a model of a 90 elbow featuring a long horizontal inlet and a short
More informationGeneralized Curvilinear Coordinates in Hybrid and Electromagnetic Codes
Advanced Methods for Space Simulations, edited by H. Usui and Y. Omura, pp. 77 89. c TERRAPUB, Tokyo, 2007. Generalized Curvilinear Coordinates in Hybrid and Electromagnetic Codes Daniel W. Swift Geophysical
More informationChapter 10. Creating 3D Objects Delmar, Cengage Learning
Chapter 10 Creating 3D Objects 2011 Delmar, Cengage Learning Objectives Extrude objects Revolve objects Manipulate surface shading and lighting Map artwork to 3D objects Extrude Objects Extrude & Bevel
More informationDiffusion Imaging Visualization
Diffusion Imaging Visualization Thomas Schultz URL: http://cg.cs.unibonn.de/schultz/ EMail: schultz@cs.unibonn.de 1 Outline Introduction to Diffusion Imaging Basic techniques Glyphbased Visualization
More informationMathematics High School Geometry An understanding of the attributes and relationships of geometric objects can be applied in diverse contexts
Mathematics High School Geometry An understanding of the attributes and relationships of geometric objects can be applied in diverse contexts interpreting a schematic drawing, estimating the amount of
More informationPhysical Modeling and Surface Detection. CS116B Chris Pollett Mar. 14, 2005.
Physical Modeling and Surface Detection CS116B Chris Pollett Mar. 14, 2005. Outline Particle Systems Physical Modeling and Visualization Classification of Visible Surface Detection Algorithms Back Face
More informationThe viscous forces on the cylinder are proportional to the gradient of the velocity field at the
Fluid Dynamics Models : Flow Past a Cylinder Flow Past a Cylinder Introduction The flow of fluid behind a blunt body such as an automobile is difficult to compute due to the unsteady flows. The wake behind
More informationIndirect Volume Rendering
Indirect Volume Rendering Visualization Torsten Möller Weiskopf/Machiraju/Möller Overview Contour tracing Marching cubes Marching tetrahedra Optimization octreebased range query Weiskopf/Machiraju/Möller
More information0. Introduction: What is Computer Graphics? 1. Basics of scan conversion (line drawing) 2. Representing 2D curves
CSC 418/2504: Computer Graphics Course web site (includes course information sheet): http://www.dgp.toronto.edu/~elf Instructor: Eugene Fiume Office: BA 5266 Phone: 416 978 5472 (not a reliable way) Email:
More informationRealtime Bounding Box Area Computation
Realtime Bounding Box Area Computation Dieter Schmalstieg and Robert F. Tobler Vienna University of Technology Abstract: The area covered by a 3D bounding box after projection onto the screen is relevant
More informationUSE OF PROPER ORTHOGONAL DECOMPOSITION TO INVESTIGATE THE TURBULENT WAKE OF A SURFACEMOUNTED FINITE SQUARE PRISM
June 30  July 3, 2015 Melbourne, Australia 9 6B3 USE OF PROPER ORTHOGONAL DECOMPOSITION TO INVESTIGATE THE TURBULENT WAKE OF A SURFACEMOUNTED FINITE SQUARE PRISM Rajat Chakravarty, Nader Moazamigoodarzi,
More informationMidterm Exam! CS 184: Foundations of Computer Graphics! page 1 of 13!
Midterm Exam! CS 184: Foundations of Computer Graphics! page 1 of 13! Student Name:!! Class Account Username:! Instructions: Read them carefully!! The exam begins at 1:10pm and ends at 2:30pm. You must
More informationNumerical Methods in Aerodynamics. Fluid Structure Interaction. Lecture 4: Fluid Structure Interaction
Fluid Structure Interaction Niels N. Sørensen Professor MSO, Ph.D. Department of Civil Engineering, Alborg University & Wind Energy Department, Risø National Laboratory Technical University of Denmark
More informationDriven Cavity Example
BMAppendixI.qxd 11/14/12 6:55 PM Page I1 I CFD Driven Cavity Example I.1 Problem One of the classic benchmarks in CFD is the driven cavity problem. Consider steady, incompressible, viscous flow in a square
More informationNumerical and theoretical analysis of shock waves interaction and reflection
Fluid Structure Interaction and Moving Boundary Problems IV 299 Numerical and theoretical analysis of shock waves interaction and reflection K. Alhussan Space Research Institute, King Abdulaziz City for
More information