Comparison of Finite Difference and Finite Element (Telemac) Models of Dublin Bay

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Dubli Istitute of Techology ARROW@DIT Presetatios Egieerig: Educatio ad Iovatio 2013-12-06 Compariso of Fiite Differece ad Fiite Elemet (Telemac) Models of Dubli Bay Garrett Keae Dubli Istitute of

1 Dubli Istitute of Techology Presetatios Egieerig: Educatio ad Iovatio Compariso of Fiite Differece ad Fiite Elemet (Telemac) Models of Dubli Bay Garrett Keae Dubli Istitute of Techology, Zeiab Bedri Uiversity College Dubli Joh O'Sulliva Uiversity College Dubli Follow this ad additioal works at: Part of the Bioresource ad Agricultural Egieerig Commos Recommeded Citatio Keae, G. (2013) Compariso of Fiite Differece ad Fiite Elemet (Telemac) Models of Dubli Bay, Joit Symposium of Irish Mechaics Society & Irish Society for Scietific & Egieerig Computatio, Advaces i Mechaics, at School of Mechaical & Materials Egieerig, Uiversity College Dubli, Belfield, Dubli 4, Irelad. This Other is brought to you for free ad ope access by the Egieerig: Educatio ad Iovatio at ARROW@DIT. It has bee accepted for iclusio i Presetatios by a authorized admiistrator of ARROW@DIT. For more iformatio, please cotact yvoe.desmod@dit.ie, arrow.admi@dit.ie, bria.widdis@dit.ie.

2 Compariso of Fiite Differece () ad Fiite Elemet (Telemac) Models of Dubli Bay Garrett Keae 1,2, Zeiab Bedri 1, Joh O Sulliva 1, Michael Brue 1 1 School of Civil, Structural ad Evirometal Egieerig, UCD 2 School of Civil ad Structural Egieerig, DIT

3 Cotext of Study CWRR, UCD (Cetre for Water Resources Research) Dubli Bay Hydrodyamic/Water Quality Models Qiag (93) - Dubli Bay Water Quality Maagemet Pla Hussey (96) - Exteded Area Euleria-Lagragia 2D Fiite Differece Model Dubli Bay Water Quality Maagemet Pla Study Howth Outfall Study Bedri (07) 3D Hydrodyamic/Water Quality Telemac Model of Ier Bay

Model Domai -6 15 to -5 50 E-W 53 10 to 53 30 N-S over 72000 grid boxes Bathymetry Admiralty Charts 1447 & 1468 Surveys for Various Studies Irish

4 Model Domai to E-W to N-S over grid boxes Bathymetry Admiralty Charts 1447 & 1468 Surveys for Various Studies Irish Hydrodata Ltd - Howth BKS Tolka Mudflats ESB Iteratioal Bull Islad Boudary Coditios North ad South - Elevatios for Sprig ad Neap Tides East Glass Wall Model Domai

5 Objectives of Study TELEMAC vs Accuracy Stability Computatioal Time Ease of use - ma hour costs. Schedule of Simulatios Code Descriptio The origial fiite differece Exteded Dubli Bay model usig a grid size of m by 92.75m. T0 The Baselie TELEMAC fiite elemet model with a uiform mesh with a resolutio of 104m betwee the odes. The four meshes used i the Telemac Covergece Study to determie the optimum mesh. T1 T2 T odes odes odes odes

6 Field Measuremets- Tides Tidal Gauges October 1998 Tidal Costituets North Wall Lighthouse North Bak Lighthouse Kish Bak Lighthouse Howth Harbour Du Laoghaire

7 Field Measuremets- Currets Sprig ad Neap Tides Locatios 1-4 Evirometal Study of Howth - Irish Hydrodata (98) Locatio of Curret Meters Locatios 5-8 Evirometal Study of Liffey Estuary ad Dubli Bay -Crisp (76)

8 Depth Averaged Fluid Equatios Cotiuity Equatio + + = 0 Mometum Equatio i x-directio + U + V ff + g + γγ θρ aw 2 si ψ k ρρ 2 U x U x 2 = 0 Mometum Equatio i y-directio + U + V + ff + g + γγ θρ aw 2 cos ψ k ρρ 2 V x V y 2 = 0

9 - Mometum Equatio DD DD = ff g γγ + θρ aw 2 si ψ + k 2 U ρρ x U x 2 +1 U 1 Ui+ i+ 2,j 1 2 a,j b Δt U 1 i 2,j 2U 1 i+ 2,j = fv i+ 1 +U 3 i+ 2,j 2,j gα 1 Δx U 1 i+ 2,j 1 k + Δx 2 α 2 γ 1 (1 α 2 )γ i+ 2,j U +1 1 i+ 2 1 i+,j 2,j U 1 i+ 2,j H i+ 1 2,j H i+ 1 2,j ξ i+1,j +1 ξ +1 i,j g(1 α 1) 2U 1 i+ 2,j + Δy 2 +U 1 i+ 2,j+1 θρ a W 2 si ψ ρρ i+ 1 2,j Δx ξ i+1,j ξ i,j + U +1 1 = 1 + i,j+ 2 2,j H 1 i+ 2,j α 2 Δt γ i+ 1 1 FF 1 gδtα 1 i+ 2,j Δx ξ i+1,j ξ i,j

10 - Cotiuity Equatio 1 + AAU i+ 1 2,j + AAV i,j+ 1 + AAU i 1 AAU i+ 1 AAU i 1 AAV i,j+ 1 AV i,j ξ 2,j 1 i+ 2,j +1 ξ 2,j 1 i 2,j +1 ξ 1 i,j+ 2 2 ξ i,j 2 2,j + AAV i,j 1 = B i,j 2 ξ i,j ξ +1 i,j

11 - Reverse Particle Trackig Euler Method U 1 i+ 2 a,j b x = x + UΔt s y = y + VΔt s

12 Bottom Frictio Parameter γ = U2 +V 2 C z 2 where C z = H 1 6

13 Surfer Grid & Pre-Processor Excel VBA Preprocessor Bathymetry - Surfer Grid

14 Vector Plots Low Water Mid-Flood

15 Vector Plots High Water Mid-Ebb

16 - Tabulated Results North Wall North Bak Du Laoghaire Kish Lighthouse Howth Harbour model Low Tide (m) measured % diff 6.6% -1.0% 4.1% -0.8% -1.2% model High Tide (m) measured % diff 8.3% 1.1% 3.1% 5.3% 2.6% model Tidal Rage (m) measured % diff 7.5% 0.1% 3.6% 2.6% 0.9% model 09:11 09:20 09:11 09:06 09:05 Time of Low Tide measured 09:07 09:06 09:01 09:11 09:45 diff (mis) model 15:16 15:18 15:18 15:14 15:13 Time of High Tide measured 15:20 15:16 15:23 15:11 15:56 diff (mis)

17 Telemac Structured Mesh Prepared with Blue Keue Caadia Hydraulics Cetre of the Natioal Research Coucil Caada

18 Telemac Structured Mesh - Results A fiite elemet solutio is geerally cosidered to be uique if the etropy coditio is satisfied (Hervouet, 2007). I the Sait-Veat equatios, the etropy is equal to the total eergy of a colum of water writte as: E = hu2 2 + g h2 2 + ggz f The etropy coditio is give by: h2 + ddd u E + g 0 2 The eergy flux ito the model domai icreases as the mesh is refied at a ope boudary. The etropy coditio is ot satisfied if the eergy flux becomes too large, resultig i the possibility of a ifiite umber of solutios of the Sait-Veat equatios ad istability.

19 Telemac Ustructured Mesh

20 Tidal Elevatios Measured, & Telemac

21 Locatio 1 Sprig Tide Velocity (m/s) Directio wrt N (deg) Magitude of Velocity Directio of Velocity

22 Locatio 2 Sprig Tide 1.5 Magitude of Velocity Velocity (m/s) Directio wrt N (deg) Directio of Velocity

23 Locatio 3 Sprig Tide Velocity (m/s) Magitude of Velocity Directio wrt N (deg) Directio of Velocity

24 Locatio 4 Sprig Tide Magitude of Velocity Velocity (m/s) Directio wrt N (deg) Directio of Velocity

25 Locatio 5 Sprig Tide Velocity (m/s) Magitude of Velocity Directio wrt N (deg) Directio of Velocity

26 Locatio 6 Sprig Tide Velocity (m/s) Magitude of Velocity Directio wrt N (deg) Directio of Velocity

27 Locatio 7 Sprig Tide Velocity (m/s) Magitude of Velocity 0.0 Directio wrt N (deg) Directio of Velocity

28 Locatio 8 Sprig Tide Velocity (m/s) Magitude of Velocity Directio wrt N (deg) Directio of Velocity

29 Simulatio Times Dell OptiPlex 780 Itel Petium CPU 2.80GHz chip. Equivalet Simulatio Time 5 cycles. Model Nodes Timestep (s) CPU time (1000) (s) ,000 T T

Finite Difference Derivations for Spreadsheet Modeling John C. Walton Modified: November 15, 2007 jcw

Finite Difference Derivations for Spreadsheet Modeling John C. Walton Modified: November 15, 2007 jcw Fiite Differece Derivatios for Spreadsheet Modelig Joh C. Walto Modified: November 15, 2007 jcw Figure 1. Suset with 11 swas o Little Platte Lake, Michiga. Page 1 Modificatio Date: November 15, 2007 Review