a state of the art review on mathematical modelling of flood propagation l.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
A state of the art review on mathematical modelling of flood propagation PowerPoint Presentation
Download Presentation
A state of the art review on mathematical modelling of flood propagation

Loading in 2 Seconds...

play fullscreen
1 / 32

A state of the art review on mathematical modelling of flood propagation - PowerPoint PPT Presentation


  • 266 Views
  • Uploaded on

A state of the art review on mathematical modelling of flood propagation . First IMPACT Workshop Wallingford, UK, 16-17 May 2002. F. Alcrudo University of Zaragoza Spain. Overview. The modelling process Mathematical models of flood propagation Solution of the Model equations Validation.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'A state of the art review on mathematical modelling of flood propagation' - soyala


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
a state of the art review on mathematical modelling of flood propagation

A state of the art review on mathematical modelling offlood propagation

First IMPACT Workshop

Wallingford, UK,

16-17 May 2002

F. Alcrudo

University of Zaragoza

Spain

overview
Overview
  • The modelling process
  • Mathematical models of flood propagation
  • Solution of the Model equations
  • Validation
the modelling process
The modelling process
  • Understanding of flow characteristics
  • Formulation of mathematical laws
  • Numerical methods
  • Programming
  • Validation of model by comparison of results against real life data
  • Prediction: Ability to FOREtell not to PASTtell
the modelling process4
The modelling process

REALITY

Analisis

Computer Simulation

& Validation

Data uncertainties

Conceptual

errors & uncertainties

Discretization errors

COMPUTER MODEL

MATHEMATICAL MODEL

Numerics &

Implementation

slide5

The flow characteristics

  • 3-D
  • time dependent
  • incompresible
  • free surface
  • fixed bed

(no erosion – deposition)

  • turbulent (very high Re)
slide6

Mathematical models

  • 3-D Navier-Stokes (DNS)
      • Chimerical
  • 3-D RANS
      • Turbulence models ?
      • Still too complex
  • Euler (inviscid)
      • Simpler, requires much less resolution
      • Could be an option soon
slide7

Mathematical models

  • Tracking of the free surface
      • VOF method (Hirt & Nichols 1981)
      • MAC method (Welch et al. 1966)
      • Moving mesh methods
slide8

NS, RANS & Euler

  • 2-D dam break and overturning waves
    • Zwart et al. 1999
    • Mohapatra et al. 1999
    • Stansby et al. (Potential) 1998
    • Stelling & Busnelli 2001...
  • River flows
    • Casulli & Stelling (Q-hydrostatic) 1998
    • Sinha et al. 1998, Ye &McCorquodale 1998...
slide9

h

v

u

Simplified mathematical models

Shallow Water Equations (SWE)

  • Depth integrated NS
  • Mass and momentum conservation in horizontal plane
  • Pseudo compressibility
slide10
Inertial & Pressure fluxes
      • Convective Momentum transport
      • Hydrostatic pressure distribution
slide11
Diffusive fluxes
      • Fluid viscosity
      • Turbulence
      • Velocity dispersion (non-uniformity)

Benqué et al. (1982)

slide12
Sources
      • Bed slope
      • Bed friction (empirical)
      • Infiltration / Aportation (Singh et al. 1998 Fiedler et al. 2000)
slide14

Issues in SWE models

  • Corrections for non-hydrostatic pressure, non-zero vertical movement
    • Boussinesq aproximation (Soares 2002)
    • Stansby and Zhou 1998 (in NS-2D-V)
    • Flow over vertical steps (Zhou et al. 2001)

(Exact solutions Alcrudo & Benkhaldoun 2001)

  • Corrections for non-uniform horizontal velocity ?

(Dispersion effects)

slide15

Issues in SWE models (cont.)

  • Turbulence modelling in 2D-H
    • Nadaoka & Yagi (1998) river flow
    • Gutting & Hutter (1998) lake circulation (K-e)
    • Gelb & Gleeson (2001) atmospheric SWE model
  • Bottom friction
    • Non-uniform unsteady friction laws ?
    • Distributed friction coefficients (Aronica et al. 1998)
    • Bottom induced horizontal shear generation (Nadaoka & Yagi 1998)
slide16

Simplified models

  • Kinematic & diffusive models
    • Arónica et al. (1998)
    • Horrit and Bates (2001)
  • Flat Pond models
    • Tous dam break inundation (Estrela 1999)
solution of the model equations restricted to swe models
Solution of the model equations(Restricted to SWE models)
  • Discretization strategies
  • Mesh configurations
  • Numerical schemes
      • Space-Time discretizations
      • Front propagation
      • Source term integration
  • Wetting and drying
slide19

Discretization strategies

  • Finite differences
      • Decaying use (less flexible)
      • Usually structured grids
      • Scheme development/testing (Liska & Wendroff 1999, Glaister 2000 ...)
      • Practical appications (Bento-Franco 1996, Heinrich et al. 2000, Aureli et al. 2000)
slide20
Finite volumes
      • Both structured & unstructured grids
      • Cell-centered or cell-vertex
      • Extremely flexible & intuitive
      • Many practical applications (CADAM 1998-1999, Brufau et al. 2000, Soares et al. 1999, Zoppou 1999)
      • Most popular
slide21
Finite elements
      • Variational formulation
        • Conceptually more complex
        • More difficult front capture operator (Ribeiro et al. 2001, Hauke 1998)
      • Practical applications
        • Hervouet 2000, Hervouet & Petitjean 1999
        • Supercritical / subcritical, tidal flows, Heniche et al. 2000
slide22

Mesh configurations

  • Structured
      • Cartesian / Boundary fitted (mappings)
      • Less flexible / Easy interpolation
  • Unstructured
      • Flexible but Indexing / Bookkeeping overheads
      • More elaborated Interpolation (Sleigh 1998, Hubbard 1999)
      • Easy refining (Sleigh 1998, Soares 1999) and adaptation (Benkhaldoun 1994, Ivanenko et al. 2000)
  • Quad-Tree
slide23

Mesh configurations

  • Quad-Tree
      • Cartesian with grid refining/adaptation
      • Hierarchical structure / Interpolation operators
      • Needs bookkeeping
      • Usually specific boundary treatments (Cartesian cut-cell approach Causon et al. 2000, 2001)
      • Practical applications (Borthwick et al. 2001)
slide24

Numerical schemes

  • Space – Time discretization
      • Space discretizations +
      • Time integration of resulting ODE
  • Time integration
      • Explicit usu 2-step, Runge-Kutta (Subject to CFL constraints)
      • Implicit (not frequent)
slide25
Front propagation
      • Shock capturing or through methods
      • Approximate Riemann solvers (Most popular Roe, WAF second)
      • Higher order interpolations + limiters (either flux or variables), TVD, ENO
      • Mostly in FV & FD but progressively incorporated into FE (Sheu & Fhang 2001)
      • Plenty of methods (or publications)
slide26
Multidimensional upwind
      • Wave recognition schemes (opposed to classical dimensional splitting)
      • Consistent Higher resolution of wave patterns
      • Usually in unstructured (cell vertex) grids (mostly triangles)
      • Considerably more expensive
      • Hubbard & Baines 1998, Brufau & Garcianavarro 2000 ...
slide27
Source term integration (bed slope)
      • Flow is source term dominated in most practical applications
      • Flux discretization must be compatible with source term
      • Source term upwinding (Bermudez & Vazquez 1994)
      • Pressure – splitting (Nujic 1995)
      • Flux lateralisation (Capart et al. 1996, Soares 2002)
      • Surface gradient method (Zhou et al. 2001)
      • Discontinuous bed topography (Zhou et al. 2002)
slide28
Wetting-drying
      • Intrinsic to flood propagation scenarios
      • Instabilities due to coupling with friction formulae and to sloping bottom (Soares 2002)
      • Threshold technique (CADAM 1998), simple, widely used but no more than a trick
      • Fictitious negative depth (Soares 2002)
      • Boundary treatment at interface (Bento-Franco 1996, Sleigh 1998), modification of bottom function (Brufau 2000)
      • Bottom function modification, ALE (Quecedo and Pastor (2002) in Taylor Galerkin FE
validation
Validation
  • Model accuracy
    • Differences between model output & real life
    • Determined with respect to experimental data
  • Accuracy loss:
    • Uncertainty Due to lack of knowledge
    • Errors Recognizable defficiencies
slide30
Main losses of accuracy in flood propagation models
    • Errors in the math description (SWE or worse)
    • Uncertainties in data (topography, friction levels, initial flood characteristics)
  • Additional errors
    • Inaccurate solution of model equations (grid refining)
slide31
Much validation work of numerical methods against analytical /other numerical solutions
      • Chippada et al., Hu et al., Aral et al. 1998
      • Holdhal et al., Liska & Wendroff , Zoppou & Roberts etc ... 1999
      • Causon et al., Wang et al., Borthwick et al. etc ... 2001
  • Validation against data from laboratory experiments
      • CADAM work, Tseng et al. 2000, Sakarya & Toykay 2000 etc ...
  • Validation against true real flooding data
      • CADAM 1999, Hervouet & Petitjean (1999), Hervouet (2000), Horritt (2000), Heinrich et al. (2001), Haider (2001)
      • Sensitiviy analysis (usually friction)
      • Urban flooding ?
conlusions
Conlusions
  • Present feasible mathematical descriptions of flood propagation are known to be erroneous but ...
      • Better mathematical models are still far ahead
  • The level of accuracy of present models has not yet been thoroughly assessed
  • There are enough methods at hand to solve the mathematical models (most are good enough)
  • Exhaustive validation programs against real data are needed