School of Computing University of Leeds
Computational PDEs Unit
A Grid-based approach to the validation and
testing of lubrication models
Christopher Goodyer
Martin Berzins
Peter Jimack
Laurence Scales (Shell Global Solutions)
Funded by DTI/EPSRC e-Science Core Programme (GR/S19486)
and Shell Global Solutions
School of Computing University of Leeds
Computational PDEs Unit
A Grid-based approach to the validation and
testing of lubrication models
Christopher Goodyer
Martin Berzins
Peter Jimack
Laurence Scales (Shell Global Solutions)
Funded by DTI/EPSRC e-Science Core Programme (GR/S19486)
and Shell Global Solutions
Presentation Overview
• Background:
– The White Rose Grid
– Elastohydrodynamic lubrication (EHL)
• A Grid-enabled Problem Solving Environment (PSE):
– Simulation
– Grid Computing
– Visualisation and Computational Steering within a PSE
• Hierarchical Parallelism
– Implementation
– Parallel simulation example
• Conclusions
Background - The White Rose Grid
Background – Elastohydrodynamic
Lubricaton (EHL)
• Applications:
High pressure contacts such as gears, valve trains, etc.
•Environmental Issues:
Energy efficiency  friction
Durability  wear
Background - EHL (cont.)
Demanding mathematics and computer
algorithms:
• Very High Loads + Small Areas
• High Pressures and Temperatures
• Deformation + Glass-like Lubricant
Lubricant  Experiment  Theory



Prediction  Computational Model
Equations for the EHL Point Contact Problem
• System of equations in 2 space dimensions
• Reynolds Equation – pressure distribution

X
•
  P   


 X  Y
  P    (  H )   (  H )  0


X
T
 Y 
Film Thickness Equation – deformation
 
H ( X , Y )  g ( X , Y )  H 00 

 
P ( x ' , y ' ) dx ' dy '
2
( X  x ' )  (Y  y ' )
• Force Balance Equation – conservation law
• Lubricant model – density, viscosity, temperature
2
Typical Point Contact Solutions
Film thickness
Pressure
Temperature
Grid-Enabled PSE - Overall Software Design
PSE (main)
PSE (collaborator)
Grid
Visualise
gViz
gViz
Simulation
Steer
Grid-Enabled PSE – Design (cont.)
PSE (main)
PSE (collaborator)
Grid
Visualise
gViz
gViz
Simulation
Steer
Grid-Enabled PSE - Simulation
• Wish to find set of lubricant model parameters (e.g.
viscosity, pressure, temperature coefficients) which best
match observed data
• Typically at least 10 such parameters to optimise
• Observations for different loadings (3), ambient
temperatures (2) and slide:roll ratios (6)
• Nonlinear optimisation of
36
RF   ( F
j 1
num
j
F
exp 2
j
)
Grid-Enabled PSE – Simulation (cont)
• Each friction evaluation is an expensive EHL calculation
• Currently use a NAG library simplex algorithm for the
multidimensional optimisation
• Scope for parallelism and use of Grid:
– Could compute all 36 frictions in parallel at each R evaluation
– More efficient to use continuation in the slide:roll parameters with
6 parallel processes
– Each of these 6 processes may themselves be implemented in
parallel and launched on different Grid resources (each using
multiple processors).
Grid-Enabled PSE – Design (cont.)
PSE (main)
PSE (collaborator)
Grid
Visualise
gViz
gViz
Simulation
Steer
Grid-Enabled PSE – Grid Computing
• Based upon use of the Globus Toolkit:
– Module provided to interrogate a GIIS server to analyse available
resources and their current status
– Job may be launched on selected resource(s) using Globus
– When job is spawned a connection is made back to the PSE (or
Grid service) indicating which node of the Grid resource the
simulation will be communicating from
• Although Grid certification is required to launch the
simulation, use of gViz libraries allow collaborators around
the world to see results of, or even steer, the simulation as
it progresses
Grid-Enabled PSE - Overall Software Design
PSE (main)
PSE (collaborator)
Grid
Visualise
gViz
gViz
Simulation
Steer
Grid-Enabled PSE – Design (cont.)
PSE (main)
PSE (collaborator)
Grid
Visualise
gViz
gViz
Simulation
Steer
Grid-Enabled PSE – Design (cont.)
PSE (main)
PSE (collaborator)
Grid
Visualise
gViz
gViz
Simulation
Steer
Grid-Enabled PSE – The PSE
• The complete PSE package is called GOSPEL (Grid
Optimisation Software for Problems of
Elastohydrodynamic Lubrication)
• It is built using NAG’s IRIS Explorer software which uses
a dataflow model
• The following IRIS Explorer map shows the three main
modules:
– GlobusSearch
– SteerGOSPEL
– VisualiseGOSPEL
Example of a typical IRIS Explorer map for the PSE:
Grid-Enabled PSE – Design (cont.)
PSE (main)
PSE (collaborator)
Grid
Visualise
gViz
gViz
Simulation
Steer
Hierarchical Parallelism
• Each friction calculation requires a costly EHL solve so
this is implemented in parallel:
– Parallel FAS multigrid
– Parallel multilevel multi-integration
• Each function evaluation requires 36 friction calculations
so these are found in parallel
– Use of continuation means that six sets of six is far more efficient
than 36 independent calculations.
Hierarchical Parallelism (cont.)
Hierarchical Parallelism (cont.)
• The following example shows typical speedups achieved…
Np
1
6
12
24
48
96
Secs.
512.0
93.3
50.0
29.3
17.6
15.1
• The loss of efficiency is due to early completion of some of
the continuation runs:
– Different processor speeds
– Different computational costs when different loads are applied
Conclusions
• Have demonstrated:
– Solution of complex and computationally expensive EHL problems
within outer optimization wrapper
– Hierarchical parallelism using Grid resources and software
– Use of Globus toolkit with MPI, NAG and gViz libraries
• Have also:
– Implemented within a PSE to allow interactive visualization and
computational steering (but not discussed here)
• Still to do:
– Better load balancing
– More versatile applications: e.g. actually designing lubricants!