Part II : Residence time


 Bernard Lyons
 1 years ago
 Views:
Transcription
1 Part II : Residence time CART  the Constituent Oriented Age and Residence time Theory p. 42
2 Residence time Widely used concept in environmental studies : 9814 references found in the Elsevier Catalog (Science Direct  Environmental Science category) over the last 10 years! Very appealing concept to biologists and decision makers! CART  the Constituent Oriented Age and Residence time Theory p. 43
3 Lagrangian approach ω!!! Mixing!!! (t 0,x 0 ) (t out,x out ) distribution of residence times Define the control domain ω Introduce a particle at (t 0,x 0 ) Compute / observe the path of this particle and register its exit time (t out,x out ) Residence time at (t 0,x 0 ) = t out t 0 CART  the Constituent Oriented Age and Residence time Theory p. 44
4 Eulerian approach m(t 0 + τ) ω Define the control domain ω Introduce a unit discharge at (t 0,x 0 ) Follow the fate of the tracer and monitor the mass m(t 0 + τ) remaining in ω Cumulative distribution of RT τ CART  the Constituent Oriented Age and Residence time Theory p. 45
5 Mean residence time m(t 0 + τ) τ m(t 0 + τ) m(t 0 ) = Mean residence time θ = 1 m(t 0 ) Fraction of the initial release with a RT larger than τ Z 0 m(t 0 + τ)dτ CART  the Constituent Oriented Age and Residence time Theory p. 46
6 Forward Eulerian procedure Solve ] + v C = [ K C + Q c C t C(t 0,x) = δ(x x 0 ) and compute m(t;t 0,x 0 ) = ZZZ ω C dv But... Open boundary conditions? CART  the Constituent Oriented Age and Residence time Theory p. 47
7 BC  version 1 Residence time = time required to leave the control domain for the first time (Bolin and Rodhe, 1973; Takeoka, 1984) Lagrangian approach : discard particles when they leave the control domain (Lagrangian approach) Eulerian approach : put C = 0 at both inflow and outflow boundaries of the control domain (if diffusion 0) θ = 0 at the open boundary. (Delhez & Deleersnijder, Ocean Dynamics) CART  the Constituent Oriented Age and Residence time Theory p. 48
8 Asymmetric Random Walk ω = ( L,L) Z α β = 1 α p (n) i : probability distribution of particles at time t n. p (n+1) i = β p (n) i 1 + α p(n) i+1, i ( L,L) Z p (n+1) L = α p (n) L+1, Equivalent to p (n) L+1 = p(n) L 1 p(n+1) L = β p (n) L 1 = 0, i.e. C = 0 outside ω CART  the Constituent Oriented Age and Residence time Theory p. 49
9 Boundary layers of the RT (1) 1D infinite domain x (,+ ) ω = [ l,+l] Constant and uniform u and κ (and Pe = ul/κ) Pe = 100 Pe = θ u/l Pe = 10 Pe = 5 1 Advection time scale Pe = 1 Pe = x/l CART  the Constituent Oriented Age and Residence time Theory p. 50
10 Boundary layers of the RT (2) Idem with tidal (1 m/s) + residual (0.1 m/s) flow ωt 2π x/l Residence time CART  the Constituent Oriented Age and Residence time Theory p. 51
11 Exposure time Residence time = time required to leave the control domain for the first time Exposure time : allow particles to exit the domain and reenter at a later time No BC at the boundary of the control domain Appropriate BC at the boundary of the computational domain CART  the Constituent Oriented Age and Residence time Theory p. 52
12 Exposure time M(t 0 + τ) ω (t 0,x 0 ) Z Θ = 1 M(t 0 + τ)dτ M(t 0 ) 0 = Measure of the time concentration to which the control region is exposed to particles originating from (t 0,x 0 ). = Exposure time τ CART  the Constituent Oriented Age and Residence time Theory p. 53
13 ET : 1D example revisited θ, Θ κ = Const. u = Const.(> 0) ω M(t;t 0,x 0 ) m(t;t 0,x 0 ) Θ(t,x) θ(t,x) CART  the Constituent Oriented Age and Residence time Theory p. 54
14 Basin average RT & ET Compute 1 V ω ZZZ ω θ(x)dx or 1 V ω ZZZ ω Θ(x)dx or solve C ] + v C = [ K C + Q c t C(t 0,x) = 1 in ω + Approp. B.C. } < θ > = 1 Z m(t;t 0,x 0 )dt = 1 Z ZZZ C dv dt < Θ > V ω t 0 V ω ω t 0 CART  the Constituent Oriented Age and Residence time Theory p. 55
15 Direct Eulerian procedure Solve and compute C t ] + v C = [ K C C(t 0,x) = δ(x x 0 ) C(t,x) = 0 on ω m(t;t 0,x 0 ) = ZZZ ω C dv But... multiple runs are needed to compute θ(t 0,x 0 ). CART  the Constituent Oriented Age and Residence time Theory p. 56
16 Operator formulation m(t;t 0,x 0 ) = <A t,t0 δ(x x 0 ),δ ω (x) > where A t,t0 = forward operator such that C(t,x) =A t,t0 δ(x x 0 ) δ ω = characteristic function of control domain ω, < f,g > = δ ω (x) = ZZZ { 1 if x ω, 0 elsewhere R 3 f(x)g(x)dv CART  the Constituent Oriented Age and Residence time Theory p. 57
17 Operator formulation (2) m(t ;t 0,x 0 ) = <A T,t0 δ(x x 0 ),δ ω (x) > = < δ(x x 0 ),A T,t 0 δ ω (x) > wherea T,t 0 = adjoint operator ofa T,t0. C T v CT t = [K CT C T (T,x) = δ ω(x) C T (t,x) = 0 on ω Adjoint state C T (t 0,x 0 ) = m(t ;t 0,x 0 ) ] CART  the Constituent Oriented Age and Residence time Theory p. 58
18 Backward procedure C ] T v CT t = [K CT CT (T,x) = δ ω(x), (t,x) = 0 on ω C T Must be integrated backward in time. A single run of the adjoint model provides m(t ;t 0,x 0 ) for a range of (t 0,x 0 ). But m(t 0 + τ;t 0,x 0 ) is required for all τ > 0, solve the adjoint problem for a range of initial conditions Ct 0 +τ(t 0 + τ,x) = δ ω (x) (unless the hydrodynamics is constant) CART  the Constituent Oriented Age and Residence time Theory p. 59
19 Backward procedure (2) Definition : D(t,τ,x) = C t+τ(t,x) = m(t + τ;t,x) D t D D+ [ ] τ + v K D = 0 D(t,0,x) = δ ω (x), D(t,τ,x) = δ(τ) on ω to be solved in a fivedimensional space. Describes the spatial and temporal variations of the cumulative distribution function of residence times m(t + τ;t, x). CART  the Constituent Oriented Age and Residence time Theory p. 60
20 Mean residence time Z 0 θ(t,x) = Z 0 m(t + τ;t,x)dτ = Z 0 D(t,τ,x)dτ D t D D+ [ ] τ + v K D = 0 D(t,0,x) = δ ω (x), D(t,τ,x) = δ(τ) on ω...dτ, assuming lim τ D(t,τ,x) = 0 θ t + δ ω + v θ+ θ(t,x) = 0 on ω [ ] K θ = 0 CART  the Constituent Oriented Age and Residence time Theory p. 61
21 Boundary conditions or D t D D+ [ ] τ + v K D θ [ ] t + δ ω + v θ+ K θ = 0 = 0 At open boundaries of the control region ω prescribe D(t,τ,x) = δ(τ 0) or θ(t,x) = 0 Residence time in ω CART  the Constituent Oriented Age and Residence time Theory p. 62
22 1D Exemple  Residence time θ κ = Const. u = Const.(> 0) ω ( ) t = 0 δ ] L,L[ + u d θ dx + θ κd2 dx 2 = 0 θ(+l) = θ( L) = 0 CART  the Constituent Oriented Age and Residence time Theory p. 63
23 Initial conditions θ [ ] t + δ ω + v θ+ K θ = 0 Must be solved by backward integration from initial conditions given at some time T. θ(t,x) =? CART  the Constituent Oriented Age and Residence time Theory p. 64
24 Initial conditions (2) τ T D(t,τ,x) known? assume D = 0 θ(t,x) = 0 θ(t,x) = T T Z 0 D(t,τ,x)dτ = Z T 0 T D(t,τ,x)dτ only material with RT < T is taken into account t CART  the Constituent Oriented Age and Residence time Theory p. 65
25 Initial conditions (3) Concentration of material with RT < T is given by C T = 1 C T where C ] T v CT t = [K CT CT (T,x) = δ ω(x) CART  the Constituent Oriented Age and Residence time Theory p. 66
26 Summary θ [ ] t + δ ω + v θ+ K θ θ(t,x) = 0, θ(t,x) = 0 on ω = 0 mean residence time C ] T + v CT t + [K CT = 0 CT (T,x) = δ ω(x), CT (t,x) = 0 on ω convergence if C T = 1 C T 1 CART  the Constituent Oriented Age and Residence time Theory p. 67
27 NWECS model x = z = 10, 10 σlevels freesurface, baroclinic, k turbulence model 10 tidal constituents, NCEP Reanalysis met. data U.K. North Sea 51 Dover Strait Belgium 51 B English Channel 358 A 0 Control region 2 France CART  the Constituent Oriented Age and Residence time Theory p. 68
28 Residence time (days) U.K France 1 days Residence time Snapshot on 15/08/ Surface value CART  the Constituent Oriented Age and Residence time Theory p. 69
29 Exposure time (days) U.K France 1 days Exposure time Snapshot on 15/08/ Surface value CART  the Constituent Oriented Age and Residence time Theory p. 70
30 Variability 120 Convergence check Exposure time Residence time /1/1983 1/5/1983 1/9/1983 1/1/1984 1/5/1984 1/9/1984 Initialization Model start Basin average RT & ET (days) 0 CART  the Constituent Oriented Age and Residence time Theory p. 71
31 RT in the mixed layer Does turbulence increase or decrease the residence time in the surface mixed layer of settling particles? CART  the Constituent Oriented Age and Residence time Theory p. 72
32 RT in the mixed layer : setup mixed layer depth = h airsea interface κ(z) w = Cte. pycnocline wc+ κ C z = 0 κ θ z = 0 C t = ( wc+ κ(z) θ ) z z C(0,z) = δ(z z 0 ) ( d wθ κ(z) dθ ) = 1 dz dz κ C z = 0 wc κ θ z = 0 CART  the Constituent Oriented Age and Residence time Theory p. 73
33 RT in the mixed layer : results θ(z) = z w + 1 w z w No diffusion Z h z exp [ Z ζ w z ] dζ dζ κ(ζ) < θ(z) < h w Infinite mixing 1 2 h w < θ = 1 h Z h 0 Factor 2 only! θ(z)dz < h w Residence time increases with turbulence! CART  the Constituent Oriented Age and Residence time Theory p. 74
34 Conclusion of part II Useful diagnostic for numerical models Flexibility : residence / exposure time Can be generalized to tracers with linear dynamics. CART  the Constituent Oriented Age and Residence time Theory p. 75
General Ocean Turbulence Model: Recent advances and future plans
General Ocean Turbulence Model: Recent advances and future plans Hans Burchard 1,3, Lars Umlauf 1 Andreas Meister 2, Thomas Neumann 1, and Karsten Bolding 3 hans.burchard@iowarnemuende.de 1. Baltic Sea
More informationIntroduction to basic principles of fluid mechanics
2.016 Hydrodynamics Prof. A.H. Techet Introduction to basic principles of fluid mechanics I. Flow Descriptions 1. Lagrangian (following the particle): In rigid body mechanics the motion of a body is described
More informationEXIT TIME PROBLEMS AND ESCAPE FROM A POTENTIAL WELL
EXIT TIME PROBLEMS AND ESCAPE FROM A POTENTIAL WELL Exit Time problems and Escape from a Potential Well Escape From a Potential Well There are many systems in physics, chemistry and biology that exist
More informationOcean Tracers. From Particles to sediment Thermohaline Circulation Past present and future ocean and climate. Only 4 hours left.
Ocean Tracers Basic facts and principles (Size, depth, S, T,, f, water masses, surface circulation, deep circulation, observing tools, ) Seawater not just water (Salt composition, Sources, sinks,, mixing
More informationMIKE 21 FLOW MODEL HINTS AND RECOMMENDATIONS IN APPLICATIONS WITH SIGNIFICANT FLOODING AND DRYING
1 MIKE 21 FLOW MODEL HINTS AND RECOMMENDATIONS IN APPLICATIONS WITH SIGNIFICANT FLOODING AND DRYING This note is intended as a general guideline to setting up a standard MIKE 21 model for applications
More informationDispersed flow reactor response to spike input
Dispersed flow reactor response to spike input Pe = c c t/t R Fraction remaining 1..9.8.7.6.5.4.3.2.1. Dispersedflow reactor performance for k =.5/day Pe = (FMT) Pe = 1 Pe = 2 Pe = 1 Pe = (PFR) 2 4 6
More informationFLUID MECHANICS IM0235 DIFFERENTIAL EQUATIONS  CB0235 2014_1
COURSE CODE INTENSITY PREREQUISITE COREQUISITE CREDITS ACTUALIZATION DATE FLUID MECHANICS IM0235 3 LECTURE HOURS PER WEEK 48 HOURS CLASSROOM ON 16 WEEKS, 32 HOURS LABORATORY, 112 HOURS OF INDEPENDENT
More informationPeriod #16: Soil Compressibility and Consolidation (II)
Period #16: Soil Compressibility and Consolidation (II) A. Review and Motivation (1) Review: In most soils, changes in total volume are associated with reductions in void volume. The volume change of the
More informationCBE 6333, R. Levicky 1 Review of Fluid Mechanics Terminology
CBE 6333, R. Levicky 1 Review of Fluid Mechanics Terminology The Continuum Hypothesis: We will regard macroscopic behavior of fluids as if the fluids are perfectly continuous in structure. In reality,
More informationLagrangian representation of microphysics in numerical models. Formulation and application to cloud geoengineering problem
Lagrangian representation of microphysics in numerical models. Formulation and application to cloud geoengineering problem M. Andrejczuk and A. Gadian University of Oxford University of Leeds Outline
More informationDear Editor. Answer to the General Comments of Reviewer # 1:
Dear Editor The paper has been fully rewritten and the title changed accordingly to Referee 1. Figures have been updated in order to answer to the wellposed questions of the reviewers. The general structure
More informationMultiBlock Gridding Technique for FLOW3D Flow Science, Inc. July 2004
FSI02TN59R2 MultiBlock Gridding Technique for FLOW3D Flow Science, Inc. July 2004 1. Introduction A major new extension of the capabilities of FLOW3D  the multiblock grid model  has been incorporated
More informationExperimental and numerical investigation of slamming of an Oscillating Wave Surge Converter in two dimensions
Experimental and numerical investigation of slamming of an Oscillating Wave Surge Converter in two dimensions T. Abadie, Y. Wei, V. Lebrun, F. Dias (UCD) Collaborating work with: A. Henry, J. Nicholson,
More informationPhysics of the Atmosphere I
Physics of the Atmosphere I WS 2008/09 Ulrich Platt Institut f. Umweltphysik R. 424 Ulrich.Platt@iup.uniheidelberg.de heidelberg.de Last week The conservation of mass implies the continuity equation:
More informationScienceDirect. Pressure Based Eulerian Approach for Investigation of Sloshing in Rectangular Water Tank
Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 144 (2016 ) 1187 1194 12th International Conference on Vibration Problems, ICOVP 2015 Pressure Based Eulerian Approach for Investigation
More informationThe First Law of Thermodynamics: Closed Systems. Heat Transfer
The First Law of Thermodynamics: Closed Systems The first law of thermodynamics can be simply stated as follows: during an interaction between a system and its surroundings, the amount of energy gained
More informationLecture 3. Turbulent fluxes and TKE budgets (Garratt, Ch 2)
Lecture 3. Turbulent fluxes and TKE budgets (Garratt, Ch 2) In this lecture How does turbulence affect the ensemblemean equations of fluid motion/transport? Force balance in a quasisteady turbulent boundary
More informationSimulation of Offshore Structures in Virtual Ocean Basin (VOB)
Simulation of Offshore Structures in Virtual Ocean Basin (VOB) Dr. Wei Bai 29/06/2015 Department of Civil & Environmental Engineering National University of Singapore Outline Methodology Generation of
More informationCHAPTER: 6 FLOW OF WATER THROUGH SOILS
CHAPTER: 6 FLOW OF WATER THROUGH SOILS CONTENTS: Introduction, hydraulic head and water flow, Darcy s equation, laboratory determination of coefficient of permeability, field determination of coefficient
More informationLecture L2  Degrees of Freedom and Constraints, Rectilinear Motion
S. Widnall 6.07 Dynamics Fall 009 Version.0 Lecture L  Degrees of Freedom and Constraints, Rectilinear Motion Degrees of Freedom Degrees of freedom refers to the number of independent spatial coordinates
More informationCFD Based Air Flow and Contamination Modeling of Subway Stations
CFD Based Air Flow and Contamination Modeling of Subway Stations Greg Byrne Center for Nonlinear Science, Georgia Institute of Technology Fernando Camelli Center for Computational Fluid Dynamics, George
More informationCOMPUTATIONAL FLOW MODEL OF WESTFALL'S 4000 OPEN CHANNEL MIXER 4115271R1. By Kimbal A. Hall, PE. Submitted to: WESTFALL MANUFACTURING COMPANY
COMPUTATIONAL FLOW MODEL OF WESTFALL'S 4000 OPEN CHANNEL MIXER 4115271R1 By Kimbal A. Hall, PE Submitted to: WESTFALL MANUFACTURING COMPANY FEBRUARY 2012 ALDEN RESEARCH LABORATORY, INC. 30 Shrewsbury
More informationOPTIMAl PREMIUM CONTROl IN A NONliFE INSURANCE BUSINESS
ONDERZOEKSRAPPORT NR 8904 OPTIMAl PREMIUM CONTROl IN A NONliFE INSURANCE BUSINESS BY M. VANDEBROEK & J. DHAENE D/1989/2376/5 1 IN A OPTIMAl PREMIUM CONTROl NONliFE INSURANCE BUSINESS By Martina Vandebroek
More informationWeierstrass Institute for Applied Analysis and Stochastics Coagulation equations and particle systems
Weierstrass Institute for Applied Analysis and Stochastics Coagulation equations and particle systems Wolfgang Wagner Mohrenstrasse 39 10117 Berlin Germany Tel. +49 30 20372 0 www.wiasberlin.de WIAS workshop,
More informationTransport of passive and active tracers in turbulent flows
Chapter 3 Transport of passive and active tracers in turbulent flows A property of turbulence is to greatly enhance transport of tracers. For example, a dissolved sugar molecule takes years to diffuse
More information1. Introduction, fluid properties (1.1, and handouts)
1. Introduction, fluid properties (1.1, and handouts) Introduction, general information Course overview Fluids as a continuum Density Compressibility Viscosity Exercises: A1 Applications of fluid mechanics
More informationTime Dependent Radiation Transport in CHNOLOGY Hohlraums Using Integral Transport Methods
FUSION TECHNOLOGY INSTITUTE Time Dependent Radiation Transport in Hohlraums Using Integral Transport Methods W I S C O N S I N K.R. Olson and D.L. Henderson June 1998 UWFDM1081 Presented at the 13th Topical
More informationImproving convergence of QuickFlow
Improving convergence of QuickFlow A Steady State Solver for the Shallow Water Equations Femke van WageningenKessels January 22, 2007 1 Background January 22, 2007 2 Background: software WAQUA QuickFlow
More informationDynamics in nanoworlds
Dynamics in nanoworlds Interplay of energy, diffusion and friction in (sub)cellular world 1 NB Queste diapositive sono state preparate per il corso di Biofisica tenuto dal Dr. Attilio V. Vargiu presso
More informationRealtime Ocean Forecasting Needs at NCEP National Weather Service
Realtime Ocean Forecasting Needs at NCEP National Weather Service D.B. Rao NCEP Environmental Modeling Center December, 2005 HYCOM Annual Meeting, Miami, FL COMMERCE ENVIRONMENT STATE/LOCAL PLANNING HEALTH
More information1D shallow convective case studies and comparisons with LES
1D shallow convective case studies and comparisons with CNRM/GMME/MésoNH 24 novembre 2005 1 / 17 Contents 1 5h6h time average vertical profils 2 2 / 17 Case description 5h6h time average vertical profils
More informationPE s Research activities and potential links to MM5. Red Ibérica MM5 Valencia 9th 10th June 2005
PE s Research activities and potential links to MM5 Red Ibérica MM5 Valencia 9th 10th June 2005 PE and its R&D Area Puertos del Estado (PE) is a Public Institution that deals with the administration of
More informationCFD Modelling of a Physical Scale Model: assessing model skill. Kristof Verelst 28112014 FHR, Antwerp
CFD Modelling of a Physical Scale Model: assessing model skill Kristof Verelst 28112014 FHR, Antwerp Introduction Introduction WL_13_61 CFD simulations of hydrodynamics for hydraulic structures (00_085)
More informationStraits of Mackinac Contaminant Release Scenarios: Flow Visualization and Tracer Simulations
Straits of Mackinac Contaminant Release Scenarios: Flow Visualization and Tracer Simulations Research Report for the National Wildlife Federation Great Lakes Regional Center By David J. Schwab, Ph.D.,
More informationIntroduction to CFD Analysis
Introduction to CFD Analysis 21 What is CFD? Computational Fluid Dynamics (CFD) is the science of predicting fluid flow, heat and mass transfer, chemical reactions, and related phenomena by solving numerically
More informationVerification Closedform Equation Comparisons
Verification Closedform Equation Comparisons GEOSLOPE International Ltd. www.geoslope.com 1400, 6336th Ave SW, Calgary, AB, Canada T2P 2Y5 Main: +1 403 269 2002 Fax: +1 403 266 4851 Introduction The
More informationUse of OpenFoam in a CFD analysis of a finger type slug catcher. Dynaflow Conference 2011 January 13 2011, Rotterdam, the Netherlands
Use of OpenFoam in a CFD analysis of a finger type slug catcher Dynaflow Conference 2011 January 13 2011, Rotterdam, the Netherlands Agenda Project background Analytical analysis of twophase flow regimes
More information17.3.1 Follow the Perturbed Leader
CS787: Advanced Algorithms Topic: Online Learning Presenters: David He, Chris Hopman 17.3.1 Follow the Perturbed Leader 17.3.1.1 Prediction Problem Recall the prediction problem that we discussed in class.
More informationFILTRATION. Water Treatment Course
FILTRATION Course, Zerihun Alemayehu FILTRATION Filtration involves the removal of suspended and colloidal particles from the water by passing it through a layer or bed of a porous granular material, such
More informationThe Navier Stokes Equations
1 The Navier Stokes Equations Remark 1.1. Basic principles and variables. The basic equations of fluid dynamics are called Navier Stokes equations. In the case of an isothermal flow, a flow at constant
More informationSolutions to the Diffusion Equation L3 11/2/06
Solutions to the Diffusion Equation 1 Solutions to Fick s Laws Fick s second law, isotropic onedimensional diffusion, D independent of concentration "c "t = D "2 c "x 2 Figure removed due to copyright
More informationOn the relative humidity of the Earth s atmosphere
On the relative humidity of the Earth s atmosphere Raymond T. Pierrehumbert The University of Chicago In collaboration with Remy Roca, LMD 1 The Many Roles of Water in Climate IR radiation, heat transport,
More information39th International Physics Olympiad  Hanoi  Vietnam  2008. Theoretical Problem No. 3
CHANGE OF AIR TEMPERATURE WITH ALTITUDE, ATMOSPHERIC STABILITY AND AIR POLLUTION Vertical motion of air governs many atmospheric processes, such as the formation of clouds and precipitation and the dispersal
More informationExpress Introductory Training in ANSYS Fluent Lecture 1 Introduction to the CFD Methodology
Express Introductory Training in ANSYS Fluent Lecture 1 Introduction to the CFD Methodology Dimitrios Sofialidis Technical Manager, SimTec Ltd. Mechanical Engineer, PhD PRACE Autumn School 2013  Industry
More informationVery High Resolution Arctic System Reanalysis for 20002011
Very High Resolution Arctic System Reanalysis for 20002011 David H. Bromwich, Lesheng Bai,, Keith Hines, and ShengHung Wang Polar Meteorology Group, Byrd Polar Research Center The Ohio State University
More informationComparison of the Vertical Velocity used to Calculate the Cloud Droplet Number Concentration in a CloudResolving and a Global Climate Model
Comparison of the Vertical Velocity used to Calculate the Cloud Droplet Number Concentration in a CloudResolving and a Global Climate Model H. Guo, J. E. Penner, M. Herzog, and X. Liu Department of Atmospheric,
More informationLS.6 Solution Matrices
LS.6 Solution Matrices In the literature, solutions to linear systems often are expressed using square matrices rather than vectors. You need to get used to the terminology. As before, we state the definitions
More informationEFFECT OF MESH SIZE ON CFD ANALYSIS OF EROSION
EFFECT OF MESH SIZE ON CFD ANALYSIS OF EROSION IN ELBOW GEOMETRY Preshit Tambey and Michael Lengyel, Jr. Faculty CoAuthor and Sponsor: Quamrul H. Mazumder Department of Computer Science, Engineering and
More informationA Response Surface Model to Predict Flammable Gas Cloud Volume in Offshore Modules. Tatiele Dalfior Ferreira Sávio Souza Venâncio Vianna
A Response Surface Model to Predict Flammable Gas Cloud Volume in Offshore Modules Tatiele Dalfior Ferreira Sávio Souza Venâncio Vianna PRESENTATION TOPICS Research Group Overview; Problem Description;
More informationIntroduction to CFD Analysis
Introduction to CFD Analysis Introductory FLUENT Training 2006 ANSYS, Inc. All rights reserved. 2006 ANSYS, Inc. All rights reserved. 22 What is CFD? Computational fluid dynamics (CFD) is the science
More informationDutch Atmospheric LargeEddy Simulation Model (DALES v3.2) CGILSS11 results
Dutch Atmospheric LargeEddy Simulation Model (DALES v3.2) CGILSS11 results Stephan de Roode Delft University of Technology (TUD), Delft, Netherlands Mixedlayer model analysis: Melchior van Wessem (student,
More informationLecture 6  Boundary Conditions. Applied Computational Fluid Dynamics
Lecture 6  Boundary Conditions Applied Computational Fluid Dynamics Instructor: André Bakker http://www.bakker.org André Bakker (20022006) Fluent Inc. (2002) 1 Outline Overview. Inlet and outlet boundaries.
More informationDESCRIPTION OF THE DRAINAGE FLOW MODEL KALM. 1. Introduction. Lohmeyer, A., Schädler, G.
Ingenieurbüro Dr.Ing. Achim Lohmeyer Karlsruhe und Dresden Strömungsmechanik Immissionsschutz Windkanaluntersuchungen An der Roßweid 3 76229 Karlsruhe Telefon: 0721 / 6 25 100 Telefax: 0721 / 6 25 10
More informationME6130 An introduction to CFD 11
ME6130 An introduction to CFD 11 What is CFD? Computational fluid dynamics (CFD) is the science of predicting fluid flow, heat and mass transfer, chemical reactions, and related phenomena by solving numerically
More informationRef. Ch. 11 in Superalloys II Ch. 8 in Khanna Ch. 14 in Tien & Caulfield
MTE 585 Oxidation of Materials Part 1 Ref. Ch. 11 in Superalloys II Ch. 8 in Khanna Ch. 14 in Tien & Caulfield Introduction To illustrate the case of high temperature oxidation, we will use Nibase superalloys.
More informationNUMERICAL ANALYSIS OF OPEN CHANNEL STEADY GRADUALLY VARIED FLOW USING THE SIMPLIFIED SAINTVENANT EQUATIONS
TASK QUARTERLY 15 No 3 4, 317 328 NUMERICAL ANALYSIS OF OPEN CHANNEL STEADY GRADUALLY VARIED FLOW USING THE SIMPLIFIED SAINTVENANT EQUATIONS WOJCIECH ARTICHOWICZ Department of Hydraulic Engineering, Faculty
More informationATM 316: Dynamic Meteorology I Final Review, December 2014
ATM 316: Dynamic Meteorology I Final Review, December 2014 Scalars and Vectors Scalar: magnitude, without reference to coordinate system Vector: magnitude + direction, with reference to coordinate system
More informationUnderstanding Complex Models using Visualization: San Bernardino Valley Groundwater Basin, Southern California
Understanding Complex Models using Visualization: San Bernardino Valley Groundwater Basin, Southern California Zhen Li and Wesley R. Danskin U.S. Geological Survey, zhenli@usgs.gov, wdanskin@usgs.gov,
More informationChoices and Applications of 2D/3D models for supporting harbour & coastal management
Choices and Applications of 2D/3D models for supporting harbour & coastal management Terug naar overzicht Rob Uittenbogaard (1,2) (1) WL Delft Hydraulics (2) Delft University of Technology ; J.M. Burgerscentre
More informationModeling Rotor Wakes with a Hybrid OVERFLOWVortex Method on a GPU Cluster
Modeling Rotor Wakes with a Hybrid OVERFLOWVortex Method on a GPU Cluster Mark J. Stock, Ph.D., Adrin Gharakhani, Sc.D. Applied Scientific Research, Santa Ana, CA Christopher P. Stone, Ph.D. Computational
More informationTheory of Chromatography
Theory of Chromatography The Chromatogram A chromatogram is a graph showing the detector response as a function of elution time. The retention time, t R, for each component is the time needed after injection
More information2.0 BASIC CONCEPTS OF OPEN CHANNEL FLOW MEASUREMENT
2.0 BASIC CONCEPTS OF OPEN CHANNEL FLOW MEASUREMENT Open channel flow is defined as flow in any channel where the liquid flows with a free surface. Open channel flow is not under pressure; gravity is the
More informationSystems Biology II: Neural Systems (580.422) Lecture 8, Linear cable theory
Systems Biology II: Neural Systems (580.422) Lecture 8, Linear cable theory Eric Young 53164 eyoung@jhu.edu Reading: D. Johnston and S.M. Wu Foundations of Cellular Neurophysiology (MIT Press, 1995).
More information( ) ( ) ( ) ( ) ( ) ( )
Problem (Q1): Evaluate each of the following to three significant figures and express each answer in SI units: (a) (0.631 Mm)/(8.60 kg) 2 (b) (35 mm) 2 *(48 kg) 3 (a) 0.631 Mm / 8.60 kg 2 6 0.631 10 m
More informationMODULE VII LARGE BODY WAVE DIFFRACTION
MODULE VII LARGE BODY WAVE DIFFRACTION 1.0 INTRODUCTION In the wavestructure interaction problems, it is classical to divide into two major classification: slender body interaction and large body interaction.
More informationIntegration of a fin experiment into the undergraduate heat transfer laboratory
Integration of a fin experiment into the undergraduate heat transfer laboratory H. I. AbuMulaweh Mechanical Engineering Department, Purdue University at Fort Wayne, Fort Wayne, IN 46805, USA Email: mulaweh@engr.ipfw.edu
More informationAppendix C  Risk Assessment: Technical Details. Appendix C  Risk Assessment: Technical Details
Appendix C  Risk Assessment: Technical Details Page C1 C1 Surface Water Modelling 1. Introduction 1.1 BACKGROUND URS Scott Wilson has constructed 13 TUFLOW hydraulic models across the London Boroughs
More informationOverset Grids Technology in STARCCM+: Methodology and Applications
Overset Grids Technology in STARCCM+: Methodology and Applications Eberhard Schreck, Milovan Perić and Deryl Snyder eberhard.schreck@cdadapco.com milovan.peric@cdadapco.com deryl.snyder@cdadapco.com
More informationFrequencydomain and stochastic model for an articulated wave power device
Frequencydomain stochastic model for an articulated wave power device J. Cândido P.A.P. Justino Department of Renewable Energies, Instituto Nacional de Engenharia, Tecnologia e Inovação Estrada do Paço
More informationConservation of Mass The Continuity Equation
Conservation of Mass The Continuity Equation The equations of motion describe the conservation of momentum in the atmosphere. We now turn our attention to another conservation principle, the conservation
More informationThompson/Ocean 420/Winter 2005 Tide Dynamics 1
Thompson/Ocean 420/Winter 2005 Tide Dynamics 1 Tide Dynamics Dynamic Theory of Tides. In the equilibrium theory of tides, we assumed that the shape of the sea surface was always in equilibrium with the
More informationValuation of EquityLinked Insurance Products and Practical Issues in Equity Modeling. March 12, 2013
Valuation of EquityLinked Insurance Products and Practical Issues in Equity Modeling March 12, 2013 The University of Hong Kong (A SOA Center of Actuarial Excellence) Session 2 Valuation of EquityLinked
More informationField Data Recovery in Tidal System Using Artificial Neural Networks (ANNs)
Field Data Recovery in Tidal System Using Artificial Neural Networks (ANNs) by Bernard B. Hsieh and Thad C. Pratt PURPOSE: The field data collection program consumes a major portion of a modeling budget.
More informationDiffusers and pollution discharge to receiving waters. Diffusers
Diffusers and pollution discharge to receiving waters Environmental Hydraulics Diffusers Small flow rates: discharge through pipe end (one jet) Large flow rates: discharge through diffuser arrangement
More informationComputational Fluid Dynamics (CFD) and Multiphase Flow Modelling. Associate Professor Britt M. Halvorsen (Dr. Ing) Amaranath S.
Computational Fluid Dynamics (CFD) and Multiphase Flow Modelling Associate Professor Britt M. Halvorsen (Dr. Ing) Amaranath S. Kumara (PhD Student), PO. Box 203, N3901, N Porsgrunn, Norway What is CFD?
More informationLecture 16  Free Surface Flows. Applied Computational Fluid Dynamics
Lecture 16  Free Surface Flows Applied Computational Fluid Dynamics Instructor: André Bakker http://www.bakker.org André Bakker (20022006) Fluent Inc. (2002) 1 Example: spinning bowl Example: flow in
More informationBasic Equations, Boundary Conditions and Dimensionless Parameters
Chapter 2 Basic Equations, Boundary Conditions and Dimensionless Parameters In the foregoing chapter, many basic concepts related to the present investigation and the associated literature survey were
More informationSimple CFD Simulations and Visualisation using OpenFOAM and ParaView. Sachiko Arvelius, PhD
Simple CFD Simulations and Visualisation using OpenFOAM and ParaView Sachiko Arvelius, PhD Purpose of this presentation To show my competence in CFD (Computational Fluid Dynamics) simulation and visualisation
More informationThe Olympus stereology system. The Computer Assisted Stereological Toolbox
The Olympus stereology system The Computer Assisted Stereological Toolbox CAST is a Computer Assisted Stereological Toolbox for PCs running Microsoft Windows TM. CAST is an interactive, userfriendly,
More informationChapter 7. Lyapunov Exponents. 7.1 Maps
Chapter 7 Lyapunov Exponents Lyapunov exponents tell us the rate of divergence of nearby trajectories a key component of chaotic dynamics. For one dimensional maps the exponent is simply the average
More informationClaudio J. Tessone. Pau Amengual. Maxi San Miguel. Raúl Toral. Horacio Wio. Eur. Phys. J. B 39, 535 (2004) http://www.imedea.uib.
Horacio Wio Raúl Toral Eur. Phys. J. B 39, 535 (2004) Claudio J. Tessone Pau Amengual Maxi San Miguel http://www.imedea.uib.es/physdept Models of Consensus vs. Polarization, or Segregation: Voter model,
More informationLecture 2 Introduction to Data Flow Analysis
Lecture 2 Introduction to Data Flow Analysis I. Introduction II. Example: Reaching definition analysis III. Example: Liveness analysis IV. A General Framework (Theory in next lecture) Reading: Chapter
More informationMark Howell Gonzaga High School, Washington, D.C.
Be Prepared for the Calculus Exam Mark Howell Gonzaga High School, Washington, D.C. Martha Montgomery Fremont City Schools, Fremont, Ohio Practice exam contributors: Benita Albert Oak Ridge High School,
More informationContents. Microfluidics  Jens Ducrée Physics: NavierStokes Equation 1
Contents 1. Introduction 2. Fluids 3. Physics of Microfluidic Systems 4. Microfabrication Technologies 5. Flow Control 6. Micropumps 7. Sensors 8. InkJet Technology 9. Liquid Handling 10.Microarrays 11.Microreactors
More informationSteady Heat Conduction
Steady Heat Conduction In thermodynamics, we considered the amount of heat transfer as a system undergoes a process from one equilibrium state to another. hermodynamics gives no indication of how long
More informationAutomatic mesh update with the solidextension mesh moving technique
Comput. Methods Appl. Mech. Engrg. 193 (2004) 2019 2032 www.elsevier.com/locate/cma Automatic mesh update with the solidextension mesh moving technique Keith Stein a, *, Tayfun E. Tezduyar b, Richard
More informationChapter 2. Derivation of the Equations of Open Channel Flow. 2.1 General Considerations
Chapter 2. Derivation of the Equations of Open Channel Flow 2.1 General Considerations Of interest is water flowing in a channel with a free surface, which is usually referred to as open channel flow.
More informationStudent Performance Q&A:
Student Performance Q&A: AP Calculus AB and Calculus BC FreeResponse Questions The following comments on the freeresponse questions for AP Calculus AB and Calculus BC were written by the Chief Reader,
More informationSTA 256: Statistics and Probability I
Al Nosedal. University of Toronto. Fall 2014 1 2 3 4 5 My momma always said: Life was like a box of chocolates. You never know what you re gonna get. Forrest Gump. Experiment, outcome, sample space, and
More information1 The Diffusion Equation
Jim Lambers ENERGY 28 Spring Quarter 200708 Lecture Notes These notes are based on Rosalind Archer s PE28 lecture notes, with some revisions by Jim Lambers. The Diffusion Equation This course considers
More informationPrinciples of groundwater flow
Principles of groundwater flow Hydraulic head is the elevation to which water will naturally rise in a well (a.k.a. static level). Any well that is not being pumped will do for this, but a well that is
More informationQuality and Reliability in CFD
Quality and Reliability in CFD Open Source Challenges Hrvoje Jasak Wikki Ltd, United Kingdom Faculty of Mechanical Engineering and Naval Architecture University of Zagreb, Croatia Quality and Reliability
More informationAccelerating Shallow Water Flow and Mass Transport Using Lattice Boltzmann Methods on GPUs. Kevin Tubbs Dell Global HPC Solutions Engineering
Accelerating Shallow Water Flow and Mass Transport Using Lattice Boltzmann Methods on GPUs Kevin Tubbs Dell Global HPC Solutions Engineering Introduction Background and Overview Role of CFD Improve Environmental
More informationUsing CloudResolving Model Simulations of Deep Convection to Inform Cloud Parameterizations in LargeScale Models
Using CloudResolving Model Simulations of Deep Convection to Inform Cloud Parameterizations in LargeScale Models S. A. Klein National Oceanic and Atmospheric Administration Geophysical Fluid Dynamics
More informationIntroduction to COMSOL. The NavierStokes Equations
Flow Between Parallel Plates Modified from the COMSOL ChE Library module rev 10/13/08 Modified by Robert P. Hesketh, Chemical Engineering, Rowan University Fall 2008 Introduction to COMSOL The following
More informationFLUID DYNAMICS. Intrinsic properties of fluids. Fluids behavior under various conditions
FLUID DYNAMICS Intrinsic properties of fluids Fluids behavior under various conditions Methods by which we can manipulate and utilize the fluids to produce desired results TYPES OF FLUID FLOW Laminar or
More informationDiffusion and Fluid Flow
Diffusion and Fluid Flow What determines the diffusion coefficient? What determines fluid flow? 1. Diffusion: Diffusion refers to the transport of substance against a concentration gradient. ΔS>0 Mass
More informationELEC 3908, Physical Electronics, Lecture 15. BJT Structure and Fabrication
ELEC 3908, Physical Electronics, Lecture 15 Lecture Outline Now move on to bipolar junction transistor (BJT) Strategy for next few lectures similar to diode: structure and processing, basic operation,
More information