Uppsala, November 24,
2011
Jacob Yström, doc. Numerical Analysis
Team leader Numerical Methods
jacob@comsol.se
Introduction to COMSOL
Multiphysics
•
COMSOL

the company and the products
•
Modelling steps in COMSOL Multiphysics
–
Live demo
•
Basic numerical techniques
•
Extensions
–
Examples: moving meshes, time

dependent h

adaption, particle
dynamics
•
Core algorithms
–
Two larger examples (CFD and RF)
World leader in multiphysics simulations
•
HQ in Stockholm.
•
16 offices in Europe, India and USA.
•
250+ employees.
•
14 000 licenses, 60 000 users.
COMSOL in Sweden
•
Development
–
Math & Computer Science
–
Numerical Methods
–
Rendering & Visualization
–
API
–
Quality & testing
•
Applications
–
Physics interfaces
–
Modules
–
Model library
•
Support
•
Sales
Traditional approach to modeling
Fluid Flow
Chemical
Reactions
Electromagnetic
Fields
Heat Transfer
Acoustics
Structural
Mechanics
The COMSOL Multiphysics approach
Fluid Flow
Chemical
Reactions
Acoustics
Electromagnetic
Fields
Heat Transfer
Structural
Mechanics
User Defined
Equations
COMSOL 4.2a Product Line
Modeling steps
•
Define geometry
–
With a
LiveLink
to CAD program, interactively or by CAD
file
import
•
Select physics (and/or mathematics)
–
Through application tailored interfaces (and/or user defined equations)
•
Generate mesh
–
Automatically, interactively, mesh import (NASTRAN)
•
Specify details
–
Material properties
–
Boundary conditions
–
Sources, sinks,...
–
Multiphysics
couplings
•
Select “Study” to perform and compute
–
Generate solver settings automatically or manually
•
Result
processing
Study
•
Study step
–
Analysis type
•
Stationary
•
Time

dependent
•
Eigenfrequency
(
eigenvalue
problem)
•
Frequency domain (harmonic assumption)
–
Physics to use
–
Mesh to use (for each geometry)
–
...
•
Multi Study step
–
Modal analysis
–
Small signal analysis
–
...
Our basic
method for PDE’s
•
Galerkin
FEM
discretization
–
With optional artificial stabilization (SD, GLS

stabilization,…)
–
Lagrange elements, Edge elements, ...
•
Standard studies
–
Stationary

> AE
•
f(
u,x
) = 0
–
Time dependent

> DAE
•
f(du/
dt,u,t,x
) = 0
–
Eigenfrequency
/Eigenvalue

> GAEP
•
(E*lambda^2 + D*lambda + K)*u=0
–
Frequency dependent (
Helmholtz
eq.)

> parametric
•
K(k)*u = L(k)
... and the basic solvers
•
Stationary
–
Fully coupled (Newton)
•
Automatic and Constant damping
–
Segregated (solve for subset of variables, iterate)
–
Pseudo time stepping (CFD)
•
Time

dependent
–
BDF solver (SUNDIALS/IDA, 1
st

5
th
order, implicit, adaptive)
–
Generalized alpha (2
nd
order, implicit,
tunable
damping, adaptive)
–
Runge

Kutta
(1
st

4
th
order, explicit, manual step length)
–
Time discrete (for CFD projection schemes)
–
Modal solver (uses
eigenfunction
expansion)
•
Algebraic eigenvalue
–
ARPACK using shift and invert mode
•
Frequency domain
–
Plain sweep (solve for each wave number k)
–
AWE (Taylor or
Padé
expansion)
–
Modal
Solver (uses
eigenfunction
expansion)
Extensions
•
Sensitivity (
f
orward and
adjoint
)
–
For stationary and time

dependent (4.3) problems
•
Optimization (NLP and LSQ)
–
SNOPT (Stanford)
–
Levenberg

Marquardt
–
For stationary and time

dependent problems (4.3)
•
h

adaption (for Stationary, Parametric and Eigenvalue problems)
–
L2

norm
–
Goal oriented (dual weighted residual)
•
h

adaption (for Time

dependent problems)
–
Fixed mesh in sub time

intervals
–
Uses a physics (or user) controlled error indicator function
•
Moving meshes
–
ALE (Arbitrary Lagrange

Eulerian
)
–
Automatic re

meshing (Parametric and Time

dependent)
•
Model control (Jobs)
–
Parametric sweep (vary any parameters in a systematic way)
–
Batch (a detachable

external process

job)
–
Cluster computing (MPI)
Extensions and more methods...
•
Particle
dynamics
–
Large system of independent ODE’s
•
Field to particle effects (one

way coupled)
•
Boundary interaction (bounce, stick, dissaper, ...)
•
Explicit and implicit time

stepping
methods
•
Far

field
evaluation
–
BEM
formulation
•
Nodal Discontinuous Galerkin method (work in progress)
–
For wave equations in the time

domain
–
High order, very memory lean, scalable, ...
–
Fully explicit time

stepping
•
Other general methods ... (work in progress)
Core algorithms
•
Linearization, evaluation and symbolic differentiation
–
Used by all the basic solvers
•
Parallel FE
assembly
–
OpenMP and MPI
•
Parallel sparse matrix
lib
–
OpenMP and MPI
•
Sparse linear systems
–
Direct; MUMPS, PARDISO, SPOOLES
–
Iterative; GMRES, FGMRES, BiCGSTAB, CG
•
Multilevel methods; AMG, GMG(hp)
•
SOR, Jacobi (standard)
•
SOR Vector (vector element Helmholtz equation)
•
SOR Gauge (ungauged magnetostatics)
•
SOR Line (boundary layer meshes)
•
Vanka (saddle point problems)
•
Krylov (Helmholtz equations)
•
LAPACK
–
BLAS; MKL, ACML
Performance example 1
•
Ahmed body (CFD benchmark model, Re>1e6)
–
k

eps Reynolds stress turbulence model
–
Mixed structured

unstructured

boundary layer mesh.
–
Size
: 2.16M dofs (linear Lagrange
elements on 1.6M mesh elements)
–
Solver: Segregated, GMRES/GMG/SOR Line
–
Memory: ~10GB
–
CPU time: 42h (

np 1), 7.5h (

np 16)
–
Accuracy C_d (drag): 2% within experimental results
Performance example 2
•
Balanced Patch Antenna for 6GHz (for cell phones, GPS etc.)
–
Study of the efficiency over a freq. range
–
No. Elems: 77k
–
Solver: BiCGStab/GMG/SOR Vector (blocked version)
–
Size: 0.47M complex valued dofs (2nd order edge elements)
–
Memory: ~2GB
–
CPU time: 307 sec (

np 4), 694 sec (

np 1)
–
A
ccuracy: 10

20% (est.)
COMSOL Multiphysics
•
Facilitates all steps in the modeling
process − defining your geometry,
meshing, specifying your physics,
solving, and then visualizing your
results.
•
Needed in order to run all add

ons.
•
Interfaces for:
–
Heat transfer
–
Structural analysis
–
Electromagnetics
–
CFD
–
Acoustics
–
Diffusion
–
PDEs
–
Unlimited
multiphysics
couplings
Heat Transfer Module
•
Handles:
–
Convection
–
Conduction
–
Radiation
•
Interfaces for:
–
Surface

to

surface radiation
–
Non

isothermal flow
–
Heat transfer in thin layers
–
Heat transfer in biological tissue
Model courtesy Continental Corporation.
AC/DC Module
•
Capacitors
•
Inductors
•
Motors & Generators
•
Cables
•
Sensors
•
EMC
•
Capacitors
•
Inductors
•
Motors & Generators
•
Cables
•
Sensors
•
EMC
Model courtesy Comet AG, Switzerland.
RF Module
•
Antennas
•
Waveguides
•
Microwave & optical
components
•
Plasmonics
•
Metamaterials
•
Seabed logging
•
Transmission lines
Plasma Module
•
All
types
of
non

nuclear
plasma
reactors
.
•
Inductively
coupled
plasmas (ICP)
•
DC discharges
•
Wave heated discharges
(Microwave plasmas)
•
Capacitively
coupled
plasmas (CCP)
Structural Mechanics Module
Model courtesy Metelli S.p.A.
•
Linear and nonlinear stress

strain
analysis
•
Thermal strains and stresses
•
Elastoplasticity and hyperelasticity
•
Contact analysis and friction
•
Buckling
•
Viscoelasticity, viscoplasticity and
creep
•
Piezoelectric effects
Geomechanics
Module
•
A specialized add

on to the Structural
Mechanics Module aimed at
modeling and simulating
geotechnical applications.
•
Interfaces to study plasticity,
deformation, and failure of soils and
rocks, as well as their interaction with
concrete and human

made
structures.
MEMS Module
Model courtesy VTT Microtechnologies Anturit.
•
Resonators
•
Actuators
•
Sensors
•
Piezoelectric
devices
•
Accelerometers
•
Lab

on

chips
•
Transducers
•
BAW/SAW devices
Acoustics Module
•
Speakers
•
Microphones
•
Transducers
•
Mufflers
•
Sound barriers
•
Building acoustics
CFD Module
•
Laminar
flow
•
K

turbulence model, including
low Re
•
Single

and multiphase flow
•
Porous media flow
•
High Mach Number flow
•
Thin Film flow
•
Rotating machinery
•
K

omega (4.2a

October)
•
Euler

Euler (4.2a

October)
Microfluidics
Module
•
Electrokinetic
flow
•
Creeping flow
•
Two

phase flow with level set
and phase field
•
Wetted walls
•
Surface tension effects
•
Fluid

Structure Interaction
Subsurface Flow Module
Model courtesy VTT Technical
Research Centre of Finland.
•
Oil& Gas flow in porous media
•
Groundwater flow
•
Pollution through soil
•
Petroleum extraction analysis
•
Poroelastic
compaction
Chemical Reaction Engineering Module
•
Is tailor

made to study reacting
systems including the effects of
material and energy transport.
•
The Chemical Engineering
Module and the Reaction
Engineering Module have been
replaced with the new Chemical
Reaction Engineering Module.
Batteries & Fuel Cells Module
•
Fuel cells
•
Alkaline
•
Molten Carbonate (MCFC)
•
Direct Methanol (DMFC)
•
Proton Exchange Membrane
(PEMFC)
•
Solid Oxid (SOFC)
•
Batteries
•
Lithium ion
•
Nickel hydride
•
Lead acid
Electrodeposition
Module
•
Enhancement of electrical and
thermal conductivity
–
Printed circuit boards, electrical contacts, and cooling devices
•
Protection of metal parts
–
Corrosion protection of nuts, bolts, and other components
–
Wear resistance coatings on bearings and shafts
•
Decoration of metals and plastics
–
Chromium coatings of automotive parts
–
Nobel metals on jewelry and tableware
•
Electroforming of parts with thin
complex shapes
–
Manufacturing of thin screens and shaver heads
–
Manufacturing of MEMS devices
Material Library
•
2500 different materials
•
Up to 24 different properties per
material.
•
Most are temperature dependent.
Optimization Module
•
Topology optimization
•
Inverse modeling
•
Based on SNOPT code by Stanford
University and University of
California San Diego
Particle Tracing Module
•
Computes the trajectory of
particles in a fluid or
electromagnetic field, including
particle

field interactions
•
Applications include:
–
Flow visualization
–
Mixing
–
Spraying
–
Particle separation
–
Mass spectrometry
–
Ion optics
–
Beam physics,
–
Ion energy distribution functions
–
Acoustic streaming
LiveLink
TM
for MATLAB
®
•
Enables scripting.
•
Save your COMSOL files as MATLAB
M

files.
•
Manipulate the M

file and call your
own functions.
•
Interface COMSOL Multiphysics
simulations to computations
performed in other simulators.
CAD Import Module
•
Brings in all major CAD formats
directly into the COMSOL Desktop:
–
ACIS
®
(.sat, .
sab
)
–
Parasolid
®
(.
x_t
, .
x_b
, .
xmt_bin
)
–
STEP (.step)
–
IGES (.
igs
)
LiveLink
TM
for SolidWorks
®
Model courtesy Comet AG, Switzerland.
•
Associative connection between
COMSOL Multiphysics and
SolidWorks.
•
Parametric sweeps and design
optimization directly from within
SolidWorks.
LiveLink
TM
for Inventor
®
•
Associative connection between
COMSOL Multiphysics and Inventor.
•
Parametric sweeps and design
optimization directly from within
Inventor.
LiveLink
TM
for Pro/ENGINEER
®
•
Associative connection between
COMSOL Multiphysics and
Pro/ENGINEER.
•
Parametric sweeps and design
optimization directly from within
Pro/ENGINEER.
LiveLink
TM
for
AutoCAD
®
•
Associative connection between
COMSOL Multiphysics and
AutoCAD.
•
Parametric sweeps and design
optimization directly from within
AutoCAD.
The picture shows a direct currents
simulation where a foil wire conductor
is represented as a surface in AutoCAD.
LiveLink
TM
for
SpaceClaim
®
•
Associative connection between
COMSOL Multiphysics and
SpaceClaim
.
•
Parametric sweeps and design
optimization directly from within
SpaceClaim
.
The picture shows a thermal simulation
of an exhaust manifold where the geometry
is synchronized between COMSOL and
SpaceClaim.
LiveLink
TM
for
Creo
TM
Parametric
•
Associative connection between
COMSOL Multiphysics and
Creo
Parametric.
•
Parametric sweeps and design
optimization directly from within
Creo
Parametric.
Streamlines showing the velocity into the impeller and
housing of an industrial fan. Model courtesy of
Gianluca
Argentini
,
Riello
Burners, Italy.
COMSOL is Expanding!
Comments 0
Log in to post a comment