# Flow Visualisation - Background. CITS4241 Visualisation Lectures 20 and 21

Size: px
Start display at page:

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, multi-variate data. Do this accurately, and Be computationally tractable 2 Flow data in an N-dimensional space can be univariate (N-dimensional scalar fields), N-variate (N-dimensional vector fields) or even N 2 -variate (N-dimensional 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 Navier-Stokes 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! Post-visualisation is usually performed, I.e. Data are saved first, and visualisation is carried out later Post-visualisation 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. Sub-samples the saved data at lower grid resolution so that more time steps can fit in memory Not favoured approach because it is expensive to sub-sample, and resolution of the flow is poor Important flow features, eg vortices, can be missed 7 8 2

3 Post-visualisation (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 cross-section encodes cross flow divergence. Streamtubes (cont.) another example The streamtube has hexagonal cross-seciton A streamline and streamribbon are added for comparison and stream ribbons or stream tubes are arguably better still. Streampolygon (cross-section 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 user-defined 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 N-variate 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

### 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

### Lecture 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

### Flow 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

### Vector 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

### Chapter 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

### 8. 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 ) Second-order tensor often represented by matrix Examples:

### Vector 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

### Data 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

### Flow 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

### 3D 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

### Vector Visualization

Vector Visualization Vector Visulization Divergence and Vorticity Vector Glyphs Vector Color Coding Displacement Plots Stream Objects Texture-Based Vector Visualization Simplified Representation of Vector

### A 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

### Using 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

### Scaling the Topology of Symmetric, Second-Order Planar Tensor Fields

Scaling the Topology of Symmetric, Second-Order Planar Tensor Fields Xavier Tricoche, Gerik Scheuermann, and Hans Hagen University of Kaiserslautern, P.O. Box 3049, 67653 Kaiserslautern, Germany E-mail:

### Part I: Theoretical Background and Integration-Based Methods

Large Vector Field Visualization: Theory and Practice Part I: Theoretical Background and Integration-Based Methods Christoph Garth Overview Foundations Time-Varying Vector Fields Numerical Integration

### mjb 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

### CIS 467/602-01: Data Visualization

CIS 467/602-01: 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

### An 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

### Volume 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

### Vector 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)

### Lecture 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

### Chapter 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

### Introduction 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

### Vector Visualization

Vector Visualization 5-1 Vector Algorithms Vector data is a three-dimensional representation of direction and magnitude. Vector data often results from the study of fluid flow, or when examining derivatives,

### 11/1/13. 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

### Visualization. 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

### Vector 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

### Fundamental Algorithms

Fundamental Algorithms Fundamental Algorithms 3-1 Overview This chapter introduces some basic techniques for visualizing different types of scientific data sets. We will categorize visualization methods

### Lecture 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

### FLUID 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

### Lecture 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

### Data Visualization (CIS/DSC 468)

Data Visualization (CIS/DSC 468) Vector Visualization Dr. David Koop Visualizing Volume (3D) Data 2D visualization slice images (or multi-planar reformating MPR) Indirect 3D visualization isosurfaces (or

### Planes 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 plane-slicing-cone picture discussed in the introduction. The relationship between the

### System 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

### Hierarchical 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

### DISCONTINUOUS 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, high-order finite

### Scientific 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

### Scientific 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.,

### Visualization Computer Graphics I Lecture 20

15-462 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/15-462/fall03

### FLOWING 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

### Chapter 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]

### Vector 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

### MAE 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

### MESHLESS SOLUTION OF INCOMPRESSIBLE FLOW OVER BACKWARD-FACING STEP

Vol. 12, Issue 1/2016, 63-68 DOI: 10.1515/cee-2016-0009 MESHLESS SOLUTION OF INCOMPRESSIBLE FLOW OVER BACKWARD-FACING STEP Juraj MUŽÍK 1,* 1 Department of Geotechnics, Faculty of Civil Engineering, University

### Visualization Computer Graphics I Lecture 20

15-462 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/

### Visualization, 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 Euler-integration Runge-Kutta-integration

### Flow Visualization: The State-of-the-Art

Flow Visualization: The State-of-the-Art The Visual and Interactive Computing Group Computer Science Department Swansea University Swansea, Wales, UK 1 Overview Introduction to Flow Visualization (FlowViz)

### Course 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

Texture Advection Ronald Peikert SciVis 2007 - Texture Advection 6-1 Texture advection Motivation: dense visualization of vector fields, no seed points needed. Methods for static fields: LIC - Line integral

### 1 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

### Prof. 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 (look-and-move visual grasping) low level

### Over 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

### Height Fields and Contours Scalar Fields Volume Rendering Vector Fields [Angel Ch. 12] April 23, 2002 Frank Pfenning Carnegie Mellon University

15-462 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/

### Introduction to CFX. Workshop 2. Transonic Flow Over a NACA 0012 Airfoil. WS2-1. ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.

Workshop 2 Transonic Flow Over a NACA 0012 Airfoil. Introduction to CFX WS2-1 Goals The purpose of this tutorial is to introduce the user to modelling flow in high speed external aerodynamic applications.

### ACGV 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

### Introduction 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

### CP 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

### Data 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

### Chapter 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 two-variable scalar function z = f (x, y), which is discussed in

### 1. 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,...

### Scalar Visualization

Scalar Visualization 5-1 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,

### Flow 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

### Scalar 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

### Surface Representations of Two- and Three-Dimensional. Fluid Flow Topology

Surface Representations of Two- and Three-Dimensional Fluid Flow Topology J. L. Helman Lambertus Hesselink Department of Applied Physics Departments of Aeronautics/Astronautics and Electrical Engineering

### Visualisation of uncertainty. Kai-Mikael Jää-Aro

Visualisation of uncertainty Kai-Mikael Jää-Aro 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

### Visualization. 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

### NUMERICAL 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)

### Visualization 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

### Shape 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

### Separation in three-dimensional steady flows. Part 2 : DETACHMENT AND ATTACHMENT SEPARATION LINES DETACHMENT AND ATTACHMENT SEPARATION SURFACES

Separation in three-dimensional steady flows Part 2 : DETACHMENT AND ATTACHMENT SEPARATION LINES DETACHMENT AND ATTACHMENT SEPARATION SURFACES Separation lines or separatrices A separation line is a skin

### Interactive 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 11794-4400

### Flow 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

### Stream 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

### computational 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

### ANSYS 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 Pre-Analysis & Start Up Governing Equation Start-Up Geometry

### Curve 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

### Chapter 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

### Lecture 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 non-spatial data Project #1 out 4 Data

### Three Dimensional Numerical Simulation of Turbulent Flow Over Spillways

Three Dimensional Numerical Simulation of Turbulent Flow Over Spillways Latif Bouhadji ASL-AQFlow Inc., Sidney, British Columbia, Canada Email: lbouhadji@aslenv.com ABSTRACT Turbulent flows over a spillway

### ds 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

### Daniel Keefe. Computer Science Department: Brown University. April 17, 2000

Artistic Metaphors for Interactive Visualization of Multi-Valued 3D Data Research Comp. Proposal Daniel Keefe Computer Science Department: Brown University April 17, 2000 1 Introduction and Motivation

### Chapter 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

### Use 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

### The Development of a Navier-Stokes Flow Solver with Preconditioning Method on Unstructured Grids

Proceedings of the International MultiConference of Engineers and Computer Scientists 213 Vol II, IMECS 213, March 13-15, 213, Hong Kong The Development of a Navier-Stokes Flow Solver with Preconditioning

### Computer Graphics I Lecture 11

15-462 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/

### Tutorial 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

### Generalized 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

### Chapter 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

### Diffusion Imaging Visualization

Diffusion Imaging Visualization Thomas Schultz URL: http://cg.cs.uni-bonn.de/schultz/ E-Mail: schultz@cs.uni-bonn.de 1 Outline Introduction to Diffusion Imaging Basic techniques Glyph-based Visualization

### Mathematics 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

### Physical 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

### The 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

### Indirect Volume Rendering

Indirect Volume Rendering Visualization Torsten Möller Weiskopf/Machiraju/Möller Overview Contour tracing Marching cubes Marching tetrahedra Optimization octree-based range query Weiskopf/Machiraju/Möller

### 0. 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:

### Real-time Bounding Box Area Computation

Real-time 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

### USE OF PROPER ORTHOGONAL DECOMPOSITION TO INVESTIGATE THE TURBULENT WAKE OF A SURFACE-MOUNTED FINITE SQUARE PRISM

June 30 - July 3, 2015 Melbourne, Australia 9 6B-3 USE OF PROPER ORTHOGONAL DECOMPOSITION TO INVESTIGATE THE TURBULENT WAKE OF A SURFACE-MOUNTED FINITE SQUARE PRISM Rajat Chakravarty, Nader Moazamigoodarzi,

### Midterm 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

### Numerical 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