Using Adaptive Mesh Refinement to Model Ocean...

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

Mandli (UW Applied Math) AMR applied to ocean flows IMUM 2010, 2010-08-17 1 / 18

Outline

1 Numerical Method

2 ExamplesCircular OceanChile TsunamiStorm Surge

3 Future Work


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


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


http://www.clawpack.org/

Circular Ocean


Chile Tsunami


Storm Surge Preliminary Results


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)


Future Work



Special Thanks To:


Using Adaptive Mesh Refinement to Model Ocean...

Documents

Transcript of Using Adaptive Mesh Refinement to Model Ocean...