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Numerical Methods for Geophysical Modelling

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Status: 50-60 person-years of development by CSIRO; distributed internationally by NAG. ... general purpose (2D/3D) PDE solver using finite elements ... – PowerPoint PPT presentation

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Title: Numerical Methods for Geophysical Modelling


1
Numerical Methods for Geophysical Modelling Noel
Barton, Paul Cleary and Nick Stokes CSIRO
Mathematical and Information Sciences www.cmis.csi
ro.au/cfd
Chapman Conference Dunsborough, WA, 19-24 August
2001
2
  • Contents
  • Synopsis of three simulation tools
  • Fastflo, SPH, DEM
  • Examples of each of them

Chapman Conference Dunsborough, WA, 19-24 August
2001
3
  • Fastflo
  • Status 50-60 person-years of development by
    CSIRO distributed internationally by NAG.
  • Description
  • general purpose (2D/3D) PDE solver using finite
    elements
  • high level command language for coding of
    timestepping or nonlinearities, graphics, control
    of the computations,
  • selection of sparse matrix solvers (direct and
    iterative)
  • flexible (equations, geometry, algorithms, free
    boundaries)
  • Applications porous media flow with heat,
    stress and chemical reactions elastic waves in
    oilfields formation of ore deposits

Chapman Conference Dunsborough, WA, 19-24 August
2001
4
Mesh generation in Fastflo
triangular mesh generator linear and
quadratic approx 2D triangles,
quadrilaterals 3D tetrahedra, hexahedra
interface to third-party software
isoparametric elements deformable boundaries
block mesh generator axisymmetry
5
Derivative expressions
1 D_j A D_j U1 - Ñ.(a Ñ u) 2
A U1 au 3 A_j
D_j U1 a.Ñ u 4 D_j A_j
U1 - Ñ. (au) 5 D_j A_jk D_k
U1 - Ñ .(A Ñ u) 6 D_jAU1_j -
div (au) 7 A D_j U1_j a
div u 8 A_j U1_j a.u 9
D_j A_k D_k U1_j - div (a.Ñ u)
10 D_j A_j D_k U1_k - div (a div u)
11 D_j A_jk U1_k - div (Au)
12 A_jk D_j U1_k div (Au)
13 D_i A U1 - Ñ (au) 14 A
D_I U1 aÑ u 15 A_i U1
au 16 D_i A_j D_j U1 - Ñ (a.Ñ u)
17 D_j A_j D_i U1 - a.Ñ (Ñ u)
- (Ñ u) Ñ.a 18 D_j A_ji U1
- Ñ .(Au) 19 A_ij D_j U1 AÑ u 20
A U1_i au 21 A_j D_j U1_i
a.Ñ u 22 D_j A_j U1_i -
a.Ñ u- u div a 23 D_j A D_j U1_i
- Ñ. (a Ñ u) 24 D_j A_jk
D_k U1_i - Ñ. (A Ñ u) 25 D_i A
D_j U1_j - Ñ (a Ñ.u) 26 D_i A_j
U1_j - Ñ(a.u) 27 D_j A D_i
U1_j (Ñ a) .Ñ(div u)-Ñ (div au)
28 A_j D_i U1_j a.(Ñ u) 29
D_j A_i U1_j - a (Ñ.u) - u.Ñ a 30
A_i D_j U1_j a (Ñ.u) 31 A_ij
U1_j Au 32 D_i A_jk D_j U1_k -
Ñ.(AÑ u) 33 D_j A_jk D_i U1_k
34 D_j A_ik D_k U1_j 35 D_j A_ij
D_k U1_k 36 D_j A_ik D_j U1_k 37
D_j A_k D_j U1_k - div aÑ u 38 D_j
A_i D_j U1 - div aÑ u
38 expressions hard-wired into the package
D_j A D_j U1 - Ñ.(a Ñ u)
A_j D_j U1_i a.Ñ u
D_i A D_j U1_j - Ñ (a Ñ.u)
6
  • Smoothed Particle Hydrodynamics (SPH)
  • Status 15 person-years of development by
    CSIRO in-house code made available through
    contracts.
  • Description
  • (2D/3D) CFD solver based on particle method
    (field variables represented by point-based
    kernel approximation Lagrangian method in that
    points can move)
  • suitable for free surface flows, splashing,
    impacts
  • additional physical effects (e.g. heat
    transfer, rheology) can be readily included
  • Applications high pressure diecasting,
    injection moulding, two-phase flow in electric
    furnaces

Chapman Conference Dunsborough, WA, 19-24 August
2001
7
SPH - Smoothed Particle Hydrodynamics
SPH is a particle based method for modelling heat
and fluid flows Particle equations of motion are
derived from the Navier-Stokes equations using
smoothing or interpolation
Continuity Equation
Momentum Equation
Energy Equation
Equation of state
where
Enthalpy H
8
  • Discrete Element Method
  • Status 15 person-years of development by
    CSIRO in-house code made available through
    contracts web-based mill simulation
    pre-processor about to be released.
  • Description
  • discrete element solver for rapid granular flows
    in complex geometries
  • disks/superquadrics in 2D, spheres in 3D
  • additional physics under development, especially
    breakage
  • Applications widely applied to grinding mills
    materials handling mixing sampling separating

Chapman Conference Dunsborough, WA, 19-24 August
2001
9
Simulations using the Discrete Element Method
(DEM) Collisional force model
10
  • Fastflo demonstration examples
  • flow of water through a faulted porous material
  • displacement of faulted rock according to linear
    elasticity
  • ltlt see the demo gtgt

Chapman Conference Dunsborough, WA, 19-24 August
2001
11
  • Fastflo demonstration examples issues that
    could be included
  • coupling of flow and elasticity
  • flow in faults linked to elastic movement
  • some resistance to compression in the faults
  • sliding friction in the faults (Bingham fluid?)
  • inclusion of other physics e.g. heat, chemical
    reactions, 3D, time-dependence
  • other possibilities mantle convection, lava
    flows, magma chamber convection,
    elasto-viscoplastic flow, slab subduction

Chapman Conference Dunsborough, WA, 19-24 August
2001
12
  • SPH example
  • dam break near the Triunfo Pass near Los Angeles
  • topography obtained from US Geological Survey
    region occupies about 15 km2
  • SPH simulations, coarse resolution 60,000
    fluid particles (corresponding to fluid particle
    separation of 6 m), 80 hrs CPU (500 MHz
    processor) for 300 sec simulation
  • other possible applications tsunamis, volcanic
    eruptions, lava flows, kimberlites, lava flow,
    elasto- viscoplastic flow, direct simulation of
    flow through porous media
  • ltlt see the video gtgt

Chapman Conference Dunsborough, WA, 19-24 August
2001
13
  • Discrete Element Example
  • breakage occurs when forces within particles
    exceed a threshold new particles are generated
    (how to do this is a topic of current research)
  • breakage of particles under stress 2D
  • breakage of particles in a tumbling cube 3D
  • other related applications excavation,
    materials handling, sampling, grinding
  • ltlt see the video gtgt

Chapman Conference Dunsborough, WA, 19-24 August
2001
14
  • Summary
  • Synopsis of three simulation tools with
    possible application in geodynamics
  • Fastflo, SPH, DEM
  • An example of each has been shown.
  • Wed be happy to provide further information
    contact us on
  • www.cmis.csiro.au/cfd

Chapman Conference Dunsborough, WA, 19-24 August
2001
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