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Benchmarking (multi)wavelet-based dynamic and static non-uniform grid solvers for flood inundation modelling

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Mohammad Kazem Sharifian, Georges Kesserwani

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Department of Civil and Structural Engineering, University of Sheffield

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The 5th International Symposium on Shallow Flows

Nanjing, China, October 23-25, 2021

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Background

What is flood modeling?

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  • Using computers to predict water levels, flows, flood depth …
  • Solve 2D equations of flow
  • Calculates variables on a grid
  • Requires DTM/DEM

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Background

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Background

Uniform Grid

  • Simple
  • Regular memory access
  • Slow

Arbitrary Grid

  • Adjust resolution
  • Irregular memory access
  • Complex

Something in-between?

Non-Uniform Grid

  • Adjust resolution
  • Mixed memory access
  • Moderate complexity

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Background

Wavelet-based Non-Uniform Grid

Static Grid

Dynamic Grid

  • Adapted based on shape of the topography
  • Constant in-time
  • Adapted based on both flow variables and topography
  • Changes in-time

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Wavelet-based dynamic grid solvers

Uniform Grid Solvers

1st order

Finite Volume (FV1)

Compatible with Haar wavelets

2nd order

Discontinuous Galerkin (DG2)

Compatible with Multiwavelets

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Wavelet-based dynamic grid solvers

 

 

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Wavelet-based dynamic grid solvers

Uniform-grid solvers

DG2

FV1

Multiresolution Analysis (MRA)

Multiwavelets (MWs)

Haar wavelets (HWs)

Dynamically adaptive solvers

MWDG2

HWFV1

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Wavelet-based dynamic grid solvers

HWFV1

MWDG2

  • MWDG2 as accurate as DG2 but more efficient than FV1

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  • MWs allow more aggressive coarsening compared to HWs

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Wavelet-based static grid solvers

    • Dam break flows, shock-like wave fronts, …
    • Rapid
    • Transient flow features + Topography
    • Dynamic grid required

Highly-energetic flood-like flows

    • Catchment-scale flood modeling
    • Slow
    • Topography + Friction
    • Static grid might suffice

Fluvial/Pluvial flooding

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Wavelet-based static grid solvers

MWs

DEM

Multiresolution grid

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Wavelet-based static grid solvers

DG2

FV1

ACC

Uniform-grid solvers

Static non-uniform

grid solvers

Non-uniform DG2

Non-uniform FV1

Non-uniform ACC

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Wavelet-based static grid solvers

Dynamic solvers

Static solvers

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Application

Dynamic solvers

Static solvers

Carlisle 2005

  • vs. uniform DG2
  • H – F – C metrics

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Application

Dynamically Adaptive solvers

Static non-uniform grid generation

Carlisle 2005

  • 5 m DEM
  • Manning’s n = 0.055
  • Coarsest grid = 4 × 3
  • Max. Res. Level = 8
  • ε = 10-3

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Application

Dynamically Adaptive solvers

Static non-uniform grid generation

Carlisle 2005

HWFV1

MWDG2

MW-generated non-uniform grid

25 % fewer elements

than uniform grid

4 % fewer elements

than uniform grid

13 % fewer elements

than uniform grid

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Application

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Application

Dynamically Adaptive solvers

Carlisle 2005

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Application

Dynamically Adaptive solvers

Carlisle 2005

1.5 X

2.8 X

15 X

3.8 X

7.5 X

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Summary

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Gradually-propagating floods:

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  • Dynamically adaptive solvers -> Expensive
  • MW-based static non-uniform grid solvers -> Efficient alternatives

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    • Non-uniform FV1 -> Least accurate
    • Non-uniform DG2 -> most accurate
    • Non-uniform ACC -> Accurate and Efficient

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Thank you very much for listening!