Upload
others
View
18
Download
0
Embed Size (px)
Citation preview
logo.png
Applied CCM Motivation PISO SLIM Results Summary
A Projection Method Based Fast TransientSolver for Incompressible Turbulent Flows
Chris Sideroff
08 June 2015
Applied CCM © 2012-2015 23rd CFD Society of Canada Conference
logo.png
Applied CCM Motivation PISO SLIM Results Summary
Applied CCMI Specialize in the application, development and support of
OpenFOAM® - based softwareI Creators and maintainers of CaelusI Locations: Canada, Australia, USA
Applied CCM © 2012-2015 23rd CFD Society of Canada Conference
logo.png
Applied CCM Motivation PISO SLIM Results Summary
Motivation
Why develop another transient solver?I DES and LES attractive because RANS tends to be
problem specificI Low cost hardware + open-source software⇒ DES and
LES feasibleI Traditional transient, incompressible algorithms (PISO and
SIMPLE) do not scale well for large HPC, GPU and ManyIntegrated Core (MIC) environments
I Let’s review PISO algorithm
Applied CCM © 2012-2015 23rd CFD Society of Canada Conference
logo.png
Applied CCM Motivation PISO SLIM Results Summary
PISO OverviewPressure Implicit with Splitting of Operators (PISO)1 method:
1. Solve momentum equation (predictor step)2. Calculate intermediate velocity, u∗ (pressure dissipation
added)3. Calculate momentum fluxes4. Solve pressure equation:∇ · ( 1
Ap∇p) = ∇ · u∗
5. Correct momentum fluxes6. Correct velocity (corrector step)
Repeat steps 2 – 6 for PISO (1 – 6 for transient SIMPLE)1Isaa, R.A. 1985, “Solution of the implicitly discretised fluid flow equations by
operator splitting” J. Comp. Phys., 61, 40.
Applied CCM © 2012-2015 23rd CFD Society of Canada Conference
logo.png
Applied CCM Motivation PISO SLIM Results Summary
Fractional Step ErrorI Step 2 main issue with PISOI Predicted velocity used only to update matrix coefficients:
u∗ = 1ap
(Σ anb unb − (∇p−∇p)
)I Pseudo-velocity, u∗, is used on the RHS of pressure
equationI Therefore requires at least two corrections to make velocity
and pressure consistent
Applied CCM © 2012-2015 23rd CFD Society of Canada Conference
logo.png
Applied CCM Motivation PISO SLIM Results Summary
Pressure MatrixI Non-constant coefficients ( 1
ap) in pressure matrix affects
multi-grid solver performanceI Multi-grid agglomeration levels cached first time pressure
matrix assembledI Coefficients ( 1
ap) only valid for the first time step
I Turning off caching of agglomeration too expensive
Applied CCM © 2012-2015 23rd CFD Society of Canada Conference
logo.png
Applied CCM Motivation PISO SLIM Results Summary
SLIM OverviewSemi Linear Implicit Method (SLIM), based on projectionmethod1: decompose velocity into vortical and irrotationalcomponents.
1. Solve momentum equation (vortical velocity)2. Calculate momentum fluxes (pressure dissipation added)3. Solve pressure equation (irrotational velocity):
∆t∇2(p) = ∇ · u4. Correct momentum flux5. Correct velocity (solenoidal)
Use incremental pressure approach to recover correctboundary pressure
1Chorin, A.J. 1968, “Numerical Solution of the Navier-Stokes
Equations”,Mathematics of Computation 22: 745-762
Applied CCM © 2012-2015 23rd CFD Society of Canada Conference
logo.png
Applied CCM Motivation PISO SLIM Results Summary
Fractional Step ErrorI Velocity split into vortical and potential components - much
smaller fractional step errorI Pressure and velocity maintain stronger couplingI Continuity satisfied within one pressure solve because
predicted velocity used directly in pressure equation
Applied CCM © 2012-2015 23rd CFD Society of Canada Conference
logo.png
Applied CCM Motivation PISO SLIM Results Summary
Pressure MatrixI Pressure matrix coefficients purely geometricI Multi-grid agglomeration levels assembled during first step
now consistent for all time stepsI Significantly improves parallel scalability for multi-grid
solver
Applied CCM © 2012-2015 23rd CFD Society of Canada Conference
logo.png
Applied CCM Motivation PISO SLIM Results Summary
2D Periodic HillsI Two dimensional, stream-wise, staggered hills of
polynomial shapeI Reh = 10,595I Stream-wise and span-wise boundaries periodic. Hills and
top boundaries no slip.I Grid: ∼ 4.5 million hex cells; LES model: Smagorinsky
Applied CCM © 2012-2015 23rd CFD Society of Canada Conference
logo.png
Applied CCM Motivation PISO SLIM Results Summary
ValidationI Experimental data of Rapp (2009)I Mean and second moment components at 10 vertical rakes
Applied CCM © 2012-2015 23rd CFD Society of Canada Conference
logo.png
Applied CCM Motivation PISO SLIM Results Summary
x/h = 2I Both compare favorablyI SLIM slightly closer than PISO
Applied CCM © 2012-2015 23rd CFD Society of Canada Conference
logo.png
Applied CCM Motivation PISO SLIM Results Summary
x/h = 4I SLIM consistently closer than PISO at all locationsI Likely due to lower fractional step error
Applied CCM © 2012-2015 23rd CFD Society of Canada Conference
logo.png
Applied CCM Motivation PISO SLIM Results Summary
Simulation TimeI SLIM on average about 30% faster on modest HPC systemI Fewer total iterations of pressure equation (SLIM: 10;
PISO: 14)
# cores PISO SLIM % diff.1 2095 1550 265 988 711 2810 419 302 2820 330 231 3040 219 147 3360 216 138 36
Applied CCM © 2012-2015 23rd CFD Society of Canada Conference
logo.png
Applied CCM Motivation PISO SLIM Results Summary
Precursor SimulationI Establish turbulent conditions to use as initial condition for
wind park simulationI Start from quiescent condition. Run until fully turbulent.I Steam-wise and span-wise periodicI Grid size: 50 million hex cellsI Results courtesy of Greg Oxley at Vestas using Firestorm
super computer
Applied CCM © 2012-2015 23rd CFD Society of Canada Conference
logo.png
Applied CCM Motivation PISO SLIM Results Summary
Mean Wind ProfileI SLIM slightly more accurate than PISOI Fully turbulent condition reached sooner than PISO
Applied CCM © 2012-2015 23rd CFD Society of Canada Conference
logo.png
Applied CCM Motivation PISO SLIM Results Summary
ScalingI Consistent multi-grid agglomeration levels give SLIM
significant advantage
Applied CCM © 2012-2015 23rd CFD Society of Canada Conference
logo.png
Applied CCM Motivation PISO SLIM Results Summary
MPI ProfilingI Profiled MPI calls on 125 million cell mesh up to 4096
cores
Applied CCM © 2012-2015 23rd CFD Society of Canada Conference
logo.png
Applied CCM Motivation PISO SLIM Results Summary
Future WorkI For static grids, pressure matrix construction may be pulled
entirely from time loop to save assembly of pressure matrixevery time step
I Advantageous for GPU and MIC computing. Computepressure matrix once. Only need to transfer RHS vector
I For peta-scale core counts, solve momentum equationsexplicitly (Runga-Kutta). Combined with above, couldperform close to fully explicit codes
I Solvers have been developed and are undergoing testing
Applied CCM © 2012-2015 23rd CFD Society of Canada Conference
logo.png
Applied CCM Motivation PISO SLIM Results Summary
Summary
I SLIM significantly faster than PISO. Problem dependentbut 30-100% is typical improvement and even more forvery large HPC calculations.
I Exact velocity splitting improves both convergence andaccuracy
I Geometric pressure matrix coefficients advantageous forparallel efficiency, particularly for multi-grid solvers
I Additional modifications enable scaling to very largenumber of cores (HPC, GPU, MIC)
Applied CCM © 2012-2015 23rd CFD Society of Canada Conference
logo.png
Applied CCM Motivation PISO SLIM Results Summary
Strategic Perspective
Select research and development projects that are unique andhelp transfer knowledge to industrial applications.
I Solvers: transient, compressible, multi-phase, combustion,acoustics
I Turbulence: RANS, DES and LES, VLES, wall modelsI Sensitivity, design optimisation, and uncertainty
propagation: adjoint, tangentI Numerical acceleration and stabilisationI Platforms and architectures: HPC, GPU, MIC
Applied CCM © 2012-2015 23rd CFD Society of Canada Conference