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Dam Break Flow

Dam Break Flow. A Fully Conservative 2D Model over Evolving Geometries Ricardo Canelas Master degree student IST 14.12.09. Teton Dam 1976. Objectives:.

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Dam Break Flow

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  1. Dam Break Flow A Fully Conservative 2D Model over Evolving Geometries Ricardo Canelas Master degree student IST 14.12.09 Teton Dam 1976

  2. Objectives: To develop a 2D fully conservative model for the propagation of discontinuous flows over evolving geometries

  3. Tackle the domain definition and mesh generation issues, define a database structure susceptible to be well articulated with the discretization procedure. Gmsh (http://www.geuz.org/gmsh/) Winged Edge Data Structure

  4. Gmsh can use a simple scripting language as I/O Possible to integrate in another code the tasks of generating meshing domains, outputting results, and generating new meshes Use Gmsh as routine to: generate the initial mesh generate subsequent refined meshes using a background mesh technique that is built according to a non-real time evaluation of the spatial variation of hydrodynamic variables (height and velocities) and of the morphological parameters (slopes)

  5. Merging of altimetric information (DTM) with the “flat” mesh Efficient terrain surface discretization using a “parametric” space: a simple projection in Cartesian coordinates One condition: the DTM is a regular grid, for fast interpolation

  6. Example on an idealized surface Domain definition Gmsh Delaunay triangulation

  7. DTM merging Final surface

  8. Generationofanisotropicmesheswithbackground meshingtechniquesonGmsh Calibrateinitialmeshcharacteristiclenghts(generalizedsizeof na elementaround a point)oneachnodeaccording to definedcriteria: spacial variation of hidrodinamic variables (height and velocities) and morphological parameters (slopes)

  9. Example: linear variationofcharactisticlenghtsacording to thirdcoordinate Original meshRefinedmesh(Delaunaytriangulation)

  10. Meshtopology data structure WingedEdge data structure Basic elementisedge Highlyredundant Constanttimequeries Relativelysmallmemoryrequirements

  11. Define discretization procedure for an uncoupled solution Use of Flux-vector Splitting Finite Volume Method: - Evaluate the PDEs, in their integral form over any discrete cell and balance the fluxes through the cell edges, in an attempt to estimate the real continuous solution. -Flux-vector Splitting considers a linear separation of the flux

  12. Complete ConservationEquations Total mass Momentumin x direction Momentumin y direction Sedimentmassintransportlayer Closureequationsneeded for hb, ub, τb, Cb*andΛ – granular dynamicsandnumericalsimulation

  13. Equationdiscretization Fullsystemin a compactform Were istheindependantconservativevariables vector istheprimitivevariables vector and are thefluxvectorsin x and y direction isthesourceterms vector

  14. Troughproperintegration, andevaluationofthe integral form, the final expression for thecomputationoffluxtroughelementedgesbecomes [Ferreira, 2009]

  15. Geomorphology – codeintegrationintheuncoupled case Development of 2D code that allows the computation of bed and lateral erosion and the integration of debris volume derived from geotechnical failure in the flow, compatible with the FVM nature of the hydrodynamical code is of major importance in this work.

  16. Bederosion – Formulation Equation for themassconservationofsedimentsinthebed Closureequations(derivedfrom granular dinamics) Equilibriumconcentration Adaptationlenght

  17. Bederosion – discretizationproblems ΔZbisevaluatedintheconservationequation for thebedofthesystem, atthebarycenterofeachelement Compatibilityproblemsintheedgesdue to diferentialerosioninadjacentelements– mustdevise a conservativeway to force compatibility Free surface level remais constant, velocities are computed again in each cell to acomodate volume change Time step ΔZb2 ΔZb1

  18. Geotechnicalfailiure Geotechnicalfailiurerepresents a bigcontribuitionofsolid material to theflowinthe case ofdambreak, andshouldbeevaluatedcarefully. Theinitialaproachwillbecomparingeachelementmaximumgradientwiththecriticalvalueandperforming a rotationoftheelementon a normal to thelineofmaximumgradient, fixedonthelowestnodeoftheelement.

  19. Geotechnical Failiure model Θ=i-icrit i>icrit ΔZ1 ΔZ2

  20. GeotechnicalFailiuremodel Compatibilizedelements Volume to integrateon theflowonthenexttime

  21. Model Limitations -Instantaneous failiure and colapse; -Accuracy dependant on element size, computed not regarding this fact; Advantages -Easy to implement; -Low computing load

  22. ModelValidation -Actual case studywithresultsproducedby a 1Dmodelisavailable for directcomparison

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