Post on 25-Jul-2020
Using Adaptive Mesh Refinement to Model Ocean Flows
M.J. Berger, D.L. George, R.J. LeVeque, and K.T. Mandli
Department of Applied MathematicsUniversity of Washington
Seattle, WA, USA
IMUM, Boston, 2010-08-17
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Outline
1 Numerical Method
2 ExamplesCircular OceanChile TsunamiStorm Surge
3 Future Work
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Goals
Solve depth averaged equations
ht + (hu)x + (hv)y = 0
(hu)t +
(hu2 +
1
2gh2
)x
+ (huv)y = −ghbx −h
ρ(PA)x +
1
ρ[τsx + τbx ]
(hu)t + (huv)x +
(hv2 +
1
2gh2
)y
= −ghby −h
ρ(PA)y +
1
ρ[τsy + τby ]
Resolve ocean to inundation spatial and temporal scales
Handle arbitrary bathymetry and inundation
Determine grids based on both physical and numerical errorestimation
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Numerical Method
Wave-propagation algorithm, class of high-resolution finite volumemethods using a Godunov type scheme
Evolve grid cell averages by determining waves at edges of grid cellsRiemann solution preserves non-trivial steady states and handlesdry-states and inundation
Adaptive mesh refinement:
Structured, patch based scheme with properly nested gridsTime steps chosen to satisfy CFL condition on current gridConservative fix-ups required along boundaries using ghost cells
GeoClaw
Download at: http://www.clawpack.org/Open source research code incorporating:
Solvers for shallow water systems using finite volume methodsAdaptive mesh refinement for complex topographyDry-states and inundation handlingTools for handling multiple topography specifications
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Circular Ocean
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Circular Ocean
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Circular Ocean
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Circular Ocean
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Chile Tsunami
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Chile Tsunami
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Chile Tsunami
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Chile Tsunami
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Storm Surge Preliminary Results
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Storm Surge Preliminary Results
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Future Work
Multilayer shallow water equations:
∂
∂t(ρ1h1) +
∂
∂x(ρ1h1u1) = 0,
∂
∂t(ρ1h1u1) +
∂
∂x
(ρ1h1u
21 + gρ1
h21
2+ gρ2h1h2
)= ρ2gh2
∂h1
∂x− ρ1gh1b
′(x)
∂
∂t(ρ2h2) +
∂
∂x(ρ2h2u2) = 0,
∂
∂t(ρ2h2u2) +
∂
∂x
(ρ2h2u
22 + gρ2
h22
2
)= −ρ2gh2
∂h1
∂x− ρ2gh2b
′(x)
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Future Work
Multilayer shallow water equations:
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Future Work
Multilayer shallow water equations:
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Special Thanks To:
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