Transcript Document

Numerical Methods for Geophysical Modelling
Noel Barton, Paul Cleary and Nick Stokes
CSIRO Mathematical and Information Sciences
www.cmis.csiro.au/cfd
Chapman Conference
Dunsborough, WA, 19-24 August 2001
Contents
• Synopsis of three simulation tools:
Fastflo, SPH, DEM
• Examples of each of them
Chapman Conference
Dunsborough, WA, 19-24 August 2001
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
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
Derivative expressions
38 expressions hardwired into the package
D_j A D_j U1
u)
A_j D_j U1_i
D_i A D_j U1_j
.u)
- .(a 
a. u
-  (a
- .(a  u)
au
a. u
- . (au)
-  .(A  u)
- div (au)
a div u
a.u
- div (a. u)
- div (a div u)
- div (Au)
div (Au)
-  (au)
a u
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D_j A D_j U1
A U1
A_j D_j U1
D_j A_j U1
D_j A_jk D_k U1
D_jAU1_j
A D_j U1_j
A_j U1_j
D_j A_k D_k U1_j
D_j A_j D_k U1_k
D_j A_jk U1_k
A_jk D_j U1_k
D_i A U1
A D_I U1
A_i U1
D_i A_j D_j U1
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D_j A_j D_i U1
D_j A_ji U1
- a. ( u) - ( u) .a
-  .(Au)
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A_ij D_j U1
A U1_i
A_j D_j U1_i
D_j A_j U1_i
D_j A D_j U1_i
D_j A_jk D_k U1_i
D_i A D_j U1_j
D_i A_j U1_j
D_j A D_i U1_j
A_j D_i U1_j
D_j A_i U1_j
A_i D_j U1_j
A_ij U1_j
D_i A_jk D_j U1_k
D_j A_jk D_i U1_k
D_j A_ik D_k U1_j
D_j A_ij D_k U1_k
D_j A_ik D_j U1_k
D_j A_k D_j U1_k
D_j A_i D_j U1
A u
au
a. u
- a. u- u div a
- . (a  u)
- . (A  u)
-  (a .u)
- (a.u)
( a) .(div u)- (div au)
a.( u)
- a (.u) - u. a
a (.u)
Au
- .(A u)
-  (a. u)
- div a u
- div a u
au
Smoothed Particle Hydrodynamics (SPH)
Status: ~ 15 person-years of development by CSIRO; inhouse 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
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
Enthalpy
where
H=
Discrete Element Method
Status: ~ 15 person-years of development by CSIRO; inhouse 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
Simulations using the Discrete Element Method (DEM)
Collisional force model
Fastflo demonstration examples
1. flow of water through a faulted porous material
2. displacement of faulted rock according to linear
elasticity
<< see the demo >>
Chapman Conference
Dunsborough, WA, 19-24 August 2001
Fastflo demonstration examples – issues that
could be included:
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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
SPH example
• dam break near the Triunfo Pass near Los Angeles
• topography obtained from US Geological Survey;
region occupies about 15 km^2
• 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, elastoviscoplastic flow, direct simulation of flow through
porous media
<< see the video >>
Chapman Conference
Dunsborough, WA, 19-24 August 2001
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
<< see the video >>
Chapman Conference
Dunsborough, WA, 19-24 August 2001
Summary
• Synopsis of three simulation tools with possible
application in geodynamics:
Fastflo, SPH, DEM
• An example of each has been shown.
• We’d be happy to provide further information;
contact us on
www.cmis.csiro.au/cfd
Chapman Conference
Dunsborough, WA, 19-24 August 2001