Craven Slides

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Multi-Region Conjugate Heat/Mass Transfer

MRconjugateHeatFoam: A DirichletNeumann partitioned multi-regionconjugate heat transfer solver

Brent A. Craven1 Robert L. Campbell2

1Computational Mechanics Division

Applied Research Laboratory

Penn State University

2Noise Control and Hydroacoustics Division

Applied Research LaboratoryPenn State University

6th OpenFOAM Workshop1316 June 2011


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Outline

1 Introduction

2 Multi-region support: OpenFOAM and ParaView

3 OpenFOAM multi-region solvers (e.g., MRconjugateHeatFoam)

4 Advanced multi-region solver development

5 Advanced multi-region usage

6 Hands-on training: MRconjugateHeatFoam


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Outline

1 Introduction







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1 Introduction







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1 Introduction







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1 Introduction







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Outline

1 Introduction







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Introduction

What do we mean by multi-region multi-physicsmodeling?

- Inherently-coupled physics on disparate continua (e.g.,fluid, solid, different solids)

- Separate governing equations for each continuum/region

For example:

- Conjugate heat and mass transfer (Part 1)- Fluid-structure interaction (Part 2)

Briefly, recall that there are two approaches to solvingsuch problems:

-Monolithic:

use same primitive variables, castgoverning equations in terms of these variables, solve asingle coupled matrix equation system

- Partitioned: separate governing equations, solveseparate matrix equation systems, couple at theboundary interface, sub-iterate until coupledconvergence is reached


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Introduction




For example:



-Monolithic:


- Partitioned: separate governing equations, solveseparate matrix equation systems, couple at theboundary interface, sub-iterate until coupledconvergence is reached


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Introduction




For example:



-Monolithic:


- Partitioned: separate governing equations, solveseparate matrix equation systems, couple at theboundary interface, sub-iterate until coupled

convergence is reached


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Introduction




For example:



-Monolithic:





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Introduction




For example:



-Monolithic:





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Introduction




For example:



-Monolithic:





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Introduction




For example:



-Monolithic:





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Introduction




For example:



-Monolithic:





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Introduction




For example:



-Monolithic:





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Introduction

Newer, monolithic solution approaches in OpenFOAM were coveredearlier by Ivor Clifford (Block-Coupled Solvers)

Here, we focus on partitioned approaches using:

- Standard multi-region OpenFOAM functionality (Part 1: Conjugateheat/mass transfer)

- Custom partitioned approaches for coupling to third-party software(Part 2: FSI)

d


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Introduction





I d i


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Introduction





I d i


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Introduction





O FOAM M l i R i C S


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OpenFOAM Multi-Region Case Structure

Multi-region OpenFOAM case structure is slightly adapted from thestandard case structure

Recall the standard case structure:

O FOAM M lti R i C St t


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Multi-region case structure:

Within each fluid and solid subdirectory there exists the standardcontents (polyMesh, transportProperties, fvSchemes, fvSolution,etc.)

O FOAM M lti R i C St t


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Multi-region case structure:

Within each fluid and solid subdirectory there exists the standardcontents (polyMesh, transportProperties, fvSchemes, fvSolution,etc.)

OpenFOAM Multi Region Support


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OpenFOAM Multi-Region Support Many of the essential OpenFOAM utilities already support this

multi-region case structure:

- blockMesh -region name- decomposePar -region name- reconstructPar -region name- checkMesh -region name

If a utility does not support multi-region cases, it is quite simple to

add (e.g., checkMesh):



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ParaView Multi-Region Support


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ParaView natively supportsmulti-region OpenFOAM cases

This includes support fordifferent variables defined oneach region

Typically, it is convenient to:

- Load the multi-region case- Extract each region via Filter

-> Extract Block

- Post-process/manipulate eachregion as desired



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ParaView Multi Region Support





-> Extract Block




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-> Extract Block




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-> Extract Block- Post-process/manipulate each

region as desired



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region as desired



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u g Supp






region as desired

OpenFOAM Multi-Region Solvers


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p g

So, now weve seen how multi-region OpenFOAM cases are setup and

post-processed Now, from a developers perspective, how are multi-region solvers

constructed?

General overview of multi-region partitioned solvers:

1 Define multiple meshes, one for each region2 Create field variables on each mesh3 Solve separate governing equations on each mesh4 Multi-region coupling at the boundary interface5 Subiterate until fully-coupled solution is reached

To illustrate, lets walk through MRconjugateHeatFoam, aDirichletNeumann partitioned multi-region conjugate heat transfersolver



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p g



constructed?






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p g



constructed?






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constructed?






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constructed?






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constructed?






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constructed?




Creating Multiple (i.e., Multi-Region) Meshes


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In createMesh.H:

Create fluidMesh Create solidMesh

For comparison, see:$FOAM_SRC/OpenFOAM/include/createMesh.H

Creating Multi-Region Field Variables


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Now we need to create field variables associated with each mesh

In createFields.H:

Create fluid variables Create solid variables

Coupled Patches


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We will cover it in more detail shortly, but thepartitioned approach inherently consists ofcoupledpatch pairs :

- Coincident boundary patches, one associated with eachregion

- These are solely where the solutions on each mesh arecoupled

Since these coupled patch pairs will be usedextensively later on, lets:

- Find the coupled patches and append to a list- Check the coupled patches

Coupled Patches


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Coupled Patches


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Coupled Patches


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Coupled Patches


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Coupled Patches


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Coupled Patches


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In checkCoupledPatches.H:

Coupled PatchesAl i h kC l dP t h H


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Also in checkCoupledPatches.H:

Can also check coupled patch:- Neighbour patch names (specified by the user in the BCs)- Size/spatial extent/surface area (coincident?)- Normals/orientation- Connectivity (if conformal meshes)

Coupled PatchesAl i h kC l dP t h H


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Coupled Patches Also in checkCoupledPatches H:


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Solving Separate Governing Equations for Each Region

S f h


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So far we have:

- Defined multiple meshes

-Create separate field variables associated with each mesh

- Checked/collected coupled patch information Now, we can solve separate governing equations in each region, which

are subject to coupled boundary conditions (to be discussed)

In solveFluid.H(or equivalently in solveSolid.H):

Multi-Region Subiteration Now we need to solve the governing equation in each region multiple


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Now we need to solve the governing equation in each region multipletimes to achieve a fully-coupled solution

Thus, at each time step we subiterate until coupled convergence is

reached In MRconjugateHeatFoam.C:

Multi-Region Coupling via DirichletNeumann Partitioning


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Multi-region coupling strategy:

1 Solve fluid (Region 1) subject to the appropriateDirichlet boundary condition at the coupled interface:

T1 = T2

2 Solve solid (Region 2) subject to the appropriateNeumann boundary condition at the coupled interface:

q1 = q

2

3 ...repeat 1-2 until converged

This is known as DirichletNeumann partitioning



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T1 = T2


q1 = q

2





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T1 = T2


q1 = q

2





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T1 = T2


q1 = q

2





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T1 = T2


q1 = q

2



Multi-Region Coupling via DirichletNeumann Partitioning In MRconjugateHeatFoam DirichletNeumann partitioning is handled


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j g gwithin the provided coupledFvPatchFieldsboundary conditions

In regionCoupleTemperatureFvPatchScalarFieldthe Dirichlet condition

is satisfied:

Multi-Region Coupling via DirichletNeumann Partitioning In regionCoupleHeatFluxFvPatchScalarField the Neumann condition is


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satisfied:

Coupled Solution Convergence

Fi ll ithi th bit ti l t th t l d


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Finally, within the subiteration loop we must ensure that coupledsolution convergence is reached to know when to stop the subiterations

This is accomplished in convergenceCheck.H by:1 Looping over coupled patches2 Calculating the maximum normalized coupled patch temperature &

heat flux residuals:

3 Stop subiterations if the maximum normalized residual is less than theuser-specified converge tolerance

Thats it! Now we have a fully-coupled multi-region solver.

Coupled Solution Convergence

Finally within the subiteration loop we must ensure that coupled


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Finally, within the subiteration loop we must ensure that coupledsolution convergence is reached to know when to stop the subiterations

This is accomplished in convergenceCheck.H by:1 Looping over coupled patches2 Calculating the maximum normalized coupled patch temperature &

heat flux residuals:

3 Stop subiterations if the maximum normalized residual is less than theuser-specified converge tolerance

Thats it! Now we have a fully-coupled multi-region solver.

Advanced Multi-Region Solver DevelopmentConservative flux interpolation on non-conformal multi-region meshes


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As is, MRconjugateHeatFoam utilizes

inverse distance weightedinterpolation provided bypatchToPatchInterpolation for bothDirichlet (temperature) and Neumann(heat flux) boundary conditions

This is appropriate for temperature

....but not for heat flux (which mustbe conserved) on non-conformalboundary meshes

For accurate flux interpolation onnon-conformal meshes, aconservative scheme is recommended(e.g., ggiInterpolation)



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Advanced Multi-Region Solver DevelopmentAccelerated coupled solution convergence via dynamic relaxation

P l MR j H F i l d i l d l i


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Presently, MRconjugateHeatFoam includes a static coupled solutionrelaxation factor

Recall in regionCoupleTemperatureFvPatchScalarField.C:

However, coupled solution convergence can be accelerated via the useof a dynamic relaxation factor (e.g., using Aitkens 2 method)

This can significantly increase coupled solution convergence rates

For example, to converge to a relative tolerance of 1x105:

- Static relaxation factor: 12 14 subiterations- Aitkens method: 2 5


P tl MR j t H tF i l d t ti l d l ti


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P tl MR j t H tF i l d t ti l d l ti


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Presently MRconj gateHeatFoam incl des a static co pled sol tion


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Presently MRconjugateHeatFoam includes a static coupled solution


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Presently MRconjugateHeatFoam includes a static coupled solution


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Advanced Multi-Region UsageParallel execution of multi-region solvers

There is one main difficulty when using


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There is one main difficulty when usingmulti-region solvers in parallel: decomposition of

coupled patch pairs

This is because patchToPatchInterpolation is notcurrently parallelized (to my knowledge at least)

So, there are two ways that I know of to run in

parallel:1 Use the simple decomposition method to

decompose both meshes at the same coordinatelocation (only works for conformal meshes)

2 Use the globalFaceZones option in the

decomposeParDictto preserve the coupledpatch pairs on all processors (works fornon-conformal meshes, but some of thenecessary utilities [e.g., faceSet] do notrecognize the -region option)




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coupled patch pairs This is because patchToPatchInterpolation is not

currently parallelized (to my knowledge at least)









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Hands-On Training: MRconjugateHeatFoam

Run standard tutorial case: conjugateChannelFlow


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Investigate the effect of the coupled solution relaxation factor

- In system/coupledSolution change coupleRelaxFactor

- Try coupleRelaxFactor= 0.1, 0.5, 0.7, 1.0 Run MRconjugateHeatFoam in parallel (use the decomposeMesh and

runmePar scripts)




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runmePar scripts)




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runmePar scripts)




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runmePar scripts)




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runmePar scripts)

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