Fluent Solverset

7/26/2019 Fluent Solverset

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Fluent Inc. 2/23/01E1

FluentSoftware Training

TRN-99-003

Solver Settings


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Outlineu Using the Solver

l Setting Solver Parameters

l Convergence

n Definition

n Monitoringn Stability

n Accelerating Convergence

l Accuracy

n Grid Independence

n Adaption

u Appendix: Background

l Finite Volume Method

l Explicit vs. Implicit

l Segregated vs. Coupled

l Transient Solutions


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Modify solution

parameters or grid

NoYes

No

Set the solution parameters

Initialize the solution

Enable the solution monitors of interest

Calculate a solution

Check for convergence

Check for accuracy

Stop

Yes

Solution Procedure Overviewu Solution Parameters

l Choosing the Solver

l Discretization Schemes

u

Initializationu Convergence

l Monitoring Convergence

l Stability

n Setting Under-relaxation

n Setting Courant number

l Accelerating Convergence

u Accuracy

l Grid Independence

l Adaption


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Choosing a Solveru Choices are Coupled-Implicit, Coupled-Explicit, or Segregated (implicit)

u The Coupled solversare recommended if a strong inter-dependence exists

between density, energy, momentum, and/or species.

l e.g., high speed compressible flow or finite-rate reaction modeled flows.

l In general, the Coupled-Implicitsolver is recommended over the coupled-explicit

solver.

n Time required: Implicit solver runs roughly twice as fast.

n Memory required: Implicit solver requires roughly twice as much memory as coupled-

explicit orsegregated-implicit solvers! (Performance varies.)

l The Coupled-Explicit solver should only be used for unsteady flows when the

characteristic time scale of problem is on same order as that of the acoustics.

n e.g., tracking transient shock wave

u The Segregated (implicit) solveris preferred in all other cases.

l Lower memory requirements than coupled-implicit solver.

l Segregated approach provides flexibility in solution procedure.


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Discretization (Interpolation Methods)u Field variables (stored at cell centers) must be interpolated to the faces of

the control volumes in the FVM:

u FLUENToffers a number of interpolation schemes:

l First-Order Upwind Scheme

n easiest to converge, only first order accurate.

l Power Law Scheme

n more accurate than first-order for flows when Recell< 5 (typ. low Re flows).

l Second-Order Upwind Scheme

n uses larger stencil for 2nd order accuracy, essential with tri/tet mesh or

when flow is not aligned with grid; slower convergence

l Quadratic Upwind Interpolation (QUICK)

n applies to quad/hex mesh, useful for rotating/swirling flows, 3rd order

accurate on uniform mesh.

VSAAVVt

f

faces

fff

faces

fff

ttt

+=+

+

,)()()(


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Interpolation Methods for Pressureu Additional interpolation options are available for calculating face pressure when

using the segregated solver.

u FLUENTinterpolation schemes for Face Pressure:

l Standard

n default scheme; reduced accuracy for flows exhibiting large surface-normal pressuregradients near boundaries.

l Linear

n useful only when other options result in convergence difficulties or unphysical

behavior.

l Second-Order

n

use for compressible flows or when PRESTO! cannot be applied.l Body Force Weighted

n use when body forces are large, e.g., high Ra natural convection or highly swirling

flows.

l PRESTO!

n applies to quad/hex cells; use on highly swirling flows, flows involving porous

media, or strongly curved domains.


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Pressure-Velocity Couplingu Pressure-Velocity Coupling refers to the way mass continuity is

accounted for when using the segregated solver.

u Three methods available:

l SIMPLE

n default scheme, robust

l SIMPLEC

n Allows faster convergence for simple problems (e.g., laminar flows with

no physical models employed).

l PISO

n useful for unsteady flow problems or for meshes containing cells with

higher than average skew.


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Initializationu Iterative procedure requires that all solution variables be initialized

before calculating a solution.

SolveInitializeInitialize...

l Realistic guesses improves solution stability and accelerates convergence.

l In some cases, correctinitial guess is required:

n Example: high temperature region to initiate chemical reaction.

u Patch values for individual

variables in certain regions.

SolveInitializePatch...

l Free jet flows(patch high velocity for jet)

l Combustion problems

(patch high temperature

for ignition)


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Convergence Preliminaries: Residualsu Transport equation for can be presented in simple form:

l Coefficients ap, anbtypically depend upon the solution.

l Coefficients updated each iteration.

u At the start of each iteration, the above equality will not hold.

l The imbalance is called the residual,Rp, where:

l Rpshould become negligibleas iterations increase.

l The residuals that you monitor are summed over all cells:

n By default, the monitored residuals are scaled.

n You can also normalize the residuals.

u Residuals monitored for the coupled solver are based on the rmsvalue of

the time rate of change of the conserved variable.

l Only for coupled equations; additional scalar equations use segregated

definition.

p

nb

nbnbpp baa =+

p

nb

nbnbppp baaR +=

||=cells

pRR


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Convergenceu At convergence:

l All discrete conservation equations (momentum, energy, etc.) are

obeyed in all cells to a specified tolerance.

l Solution no longer changes with more iterations.

l Overall mass, momentum, energy, and scalar balances are obtained.

u Monitoring convergence with residuals:

l Generally, a decrease in residuals by 3 orders of magnitude indicates at

least qualitative convergence.

n Major flow features established.

l Scaled energy residual must decrease to 10-6for segregated solver.

l Scaled species residual may need to decrease to 10-5to achieve speciesbalance.

u Monitoring quantitative convergence:

l Monitor other variables for changes.

l Ensure that property conservation is satisfied.


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Convergence Monitors: Residualsu Residual plots show when the residual values have reached the

specified tolerance.

SolveMonitors Residual...

All equations converged.

10-3

10-6


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Convergence Monitors: Forces/Surfacesu In addition to residuals, you can also monitor:

l Lift, drag, or moment

SolveMonitorsForce...

l Variables or functions (e.g., surface integrals)

at a boundary or any defined surface:SolveMonitorsSurface...


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Checking for Property Conservation

u In addition to monitoring residual and variable histories, you should

also check for overall heat and mass balances.

l Net imbalance should be less than 0.1% of net flux through domain.

Report

Fluxes...


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Decreasing the Convergence Toleranceu If your monitors indicate that the solution is converged, but the

solution is still changing or has a large mass/heat imbalance:

l Reduce Convergence Criterion

or disable Check Convergence.

l Then calculate until solution

converges to the new tolerance.


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Convergence Difficultiesu Numerical instabilities can arise with an ill-posed problem, poor

quality mesh, and/or inappropriate solver settings.

l Exhibited as increasing (diverging) or stuck residuals.

l Diverging residuals imply increasing imbalance in conservation equations.

l Unconverged results can be misleading!

u Troubleshooting:

l Ensure problem is well posed.

l Compute an initial solution with

a first-order discretization scheme.

l

Decrease under-relaxation forequations having convergence

trouble (segregated).

l Reduce Courant number (coupled).

l Re-mesh or refine grid with high

aspect ratio or highly skewed cells.

Continuity equation convergence

trouble affects convergence of

all equations.


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Modifying Under-relaxation Factorsu Under-relaxation factor, , is

included to stabilize the iterative

process for the segregated solver.

u Use default under-relaxation factors

to start a calculation.

SolveControlsSolution...

u Decreasing under-relaxation for

momentumoften aids convergence.

l Default settings are aggressive but

suitable for wide range of problems.l Appropriate settings best learned

from experience.

poldpp += ,

u For coupled solvers, under-relaxation factors for equations outsidecoupled

set are modified as in segregated solver.


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Modifying the Courant Numberu Courant number defines a time

step size for steady-state problems.

l A transient term is included in the

coupled solver even for steady state

problems.

u For coupled-explicit solver:

l Stability constraints impose a

maximum limit on Courant number.

n Cannot be greater than 2.

s Default value is 1.

n Reduce Courant number when

having difficulty converging.

u

xt

=

)CFL(u For coupled-implicit solver:

l Courant number is not limited by stability constraints.

n Default is set to 5.


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Accelerating Convergence

u Convergence can be accelerated by:

l Supplying good initial conditions

n Starting from a previous solution.

l

Increasing under-relaxation factors or Courant numbern Excessively high values can lead to instabilities.

n Recommend saving case and data files before continuing iterations.

l Controlling multigrid solver settings.

n Default settings define robust Multigrid solver and typically do not need

to be changed.


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Starting from a Previous Solutionu Previous solution can be used as an initial condition when changes are

made to problem definition.

l Once initialized, additional iterations uses current data setas starting point.

Actual Problem Initial Condition

flow with heat transfer isothermal solution

natural convection lowerRa solution

combustion cold flow solution

turbulent flow Euler solution


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Multigridu The Multigrid solver accelerates convergence by using solution on

coarse mesh as starting point for solution on finer mesh.

l Influence of boundaries and far-away points are more easily transmitted to

interior of coarse mesh than on fine mesh.

l Coarse mesh defined from original mesh.n Multiple coarse mesh levels can be created.

s AMG- coarse mesh emulated algebraically.

s FAS- cell coalescing defines new grid.

a coupled-explicit solver option

n Final solution is for original mesh.

l Multigrid operates automatically in the background.

u Accelerates convergence for problems with:

l Large number of cells

l Large cell aspect ratios, e.g., x/y > 20

l Large differences in thermal conductivity

fine (original) mesh

coarse mesh

solution

transfer


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Accuracyu A converged solution is not necessarily an accurate one.

l Solve using 2nd order discretization.

l Ensure that solution is grid-independent.

n Use adaption to modify grid.

u If flow features do not seem reasonable:

l Reconsider physical models and boundary conditions.

l Examine grid and re-mesh.


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Mesh Quality and Solution Accuracyu Numerical errors are associated with calculation of cell gradients and

cell face interpolations.

u These errors can be contained:

l Use higher order discretization schemes.

l Attempt to align grid with flow.l Refine the mesh.

n Sufficient mesh density is necessary to resolve salient features of flow.

s Interpolation errors decrease with decreasing cell size.

n Minimize variations in cell size.

s Truncation error is minimized in a uniform mesh.

s Fluent provides capability to adapt mesh based on cell size variation.

n Minimize cell skewness and aspect ratio.

s In general, avoid aspect ratios higher than 5:1.

s Optimal quad/hex cells have bounded angles of 90 degrees

s Optimal tri/tet cells are equilateral.


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Determining Grid Independenceu When solution no longer changes with further grid refinement, you

have a grid-independent solution.

u Procedure:

l Obtain new grid:

n

Adapts Save original mesh before adapting.

If you know where large gradients are expected, concentrate the

original grid in that region, e.g., boundary layer.

s Adapt grid.

Data from original grid is automatically interpolated to finer grid.

n filereread-grid

andFile

Interpolate...

s Import new mesh and initialize with old solution.

l Continue calculation to convergence.

l Compare results obtained w/different grids.

l Repeat adaption/calculation procedure if necessary.


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Unsteady Flow Problemsu Transient solutions are possible with both segregated and coupled solvers.

l Solver iterates to convergence at each time level, then advances automatically.

l Solution Initialization provides initial condition, must be realistic.

u For segregated solver:

l Time step size, t, is input in Iterate panel.n t should be small enough to resolve

time dependent features and to ensure

convergence within 20 iterations.

n May need to start solution with small t.

l Number of time steps, N, is also required.

n N*t =total simulated time.l Use TUI command it # to iterate without advancing time step.

u For Coupled Solver, Courant number defines in practice:

l global time step size for coupled explicit solver.

l pseudo-time step size for coupled implicit solver.


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Summary

u Solution procedure for the segregated and coupled solvers is the same:

l Calculate until you get a converged solution.

l Obtain second-order solution (recommended).

l

Refine grid and recalculate until grid-independent solution is obtained.u All solvers provide tools for judging and improving convergence and

ensuring stability.

u All solvers provide tools for checking and improving accuracy.

u Solution accuracy will depend on the appropriateness of the physical

models that you choose and the boundary conditions that you specify.


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Appendixu Background

l Finite Volume Method

l Explicit vs. Implicit

l Segregated vs. Coupled

l Transient Solutions


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Background: Finite Volume Method - 1u FLUENTsolvers are based on the finite volume method.

l Domain is discretized into a finite set of control volumes or cells.

u General transport equation for mass, momentum, energy, etc. is

applied to eachcell and discretized. For cellp,

+=+

dVSdddV

tAAV

AAV

unsteady convection diffusion generation

Eqn.

continuity 1x-mom. u

y-mom. v

energy h

Fluid region of pipe flow

discretized into finite set of

control volumes (mesh).

control

volume

u Allequations are solved to render flow field.


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Background: Finite Volume Method - 2u Each transport equation is discretized into algebraic form. For cell p,

face f

adjacent cells, nb

cellp

u Discretized equations require information at cell centers andfaces.

l Field data (material properties, velocities, etc.) are stored at cell centers.

l Face values can be expressed in terms of local andadjacent cell values.

l Discretization accuracy depends upon stencil size.

u

The discretized equation can be expressed simply as:

l Equation is written out for every control volume in domain resulting in an

equation set.

p

nb

nbnbppbaa =+

VSAAVVt

f

faces

fff

faces

fff

t

p

tt

p +=+

+

,)()()(


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u Equation sets are solved iteratively.

l Coefficients apand anbare typically functions

of solution variables(nonlinear and coupled).

l Coefficients are written to use values of solution variables from previous

iteration.

n Linearization: removing coefficients dependencies on .

n De-coupling: removing coefficients dependencies on other solution

variables.

l Coefficients are updated with each iteration.

n For a given iteration, coefficients are constant.

s pcan either be solved explicitly or implicitly.

Background: Linearization

p

nb

nbnbpp baa =+


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u Assumptions are made about the knowledge of nb:

l Explicit linearization- unknown value in each cell computed from relations

that include only existingvalues (nb assumed known from previous

iteration).

n psolved explicitly using Runge-Kutta scheme.

l Implicit linearization- p andnb are assumed unknown and are solved

using linear equation techniques.

n Equations that are implicitly linearized tend to have less restrictive stability

requirements.

n

The equation set is solved simultaneously using a second iterative loop (e.g.,point Gauss-Seidel).

Background: Explicit vs. Implicit


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Background: Coupled vs. Segregated

u Segregated Solver

l If the only unknowns in a given equation are assumed to be for asingle

variable, then the equation set can be solved without regard for the

solution of other variables.

n coefficients apand anbare scalars.

u Coupled Solver

l If more than one variableis unknown in each equation, and each

variable is defined by its own transport equation, then the equation set is

coupledtogether.

n coefficients apand anbareNeqx Neqmatricesn is a vector of the dependent variables, {p, u, v, w, T, Y}T

p

nb

nbnbpp baa =+


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Background: Segregated Solver

u In the segregated solver, each equation is

solved separately.

u The continuity equation takes the form

of a pressure correction equation as partof SIMPLE algorithm.

u Under-relaxation factors are included in

the discretized equations.

l Included to improve stability of iterative

process.

l Under-relaxation factor, , in effect,limits change in variable from one

iteration to next:

Update properties.

Solve momentum equations (u, v, w velocity).

Solve pressure-correction (continuity) equation.

Update pressure, face mass flow rate.

Solve energy, species, turbulence, and other

scalar equations.

Converged?

Stop

No Yes

poldpp += ,


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Background: Coupled Solveru Continuity, momentum, energy, and

species are solved simultaneously in the

coupled solver.

u Equations are modified to resolve

compressible andincompressible flow.u Transient term is always included.

l Steady-state solution is formed as time

increases and transients tend to zero.

u For steady-state problem, time step is

defined by Courant number.l Stability issues limit maximum time step

size for explicit solver but not for

implicit solver.

Solve continuity, momentum, energy,

and species equations simultaneously.

Stop

No Yes

Solve turbulence and other scalar equations.

Update properties.

Converged?

u

xt

=

)CFL( CFL= Courant-Friedrichs-Lewy-numberwhere u= appropriate velocity scale

x= grid spacing


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Background: Segregated/Transientu Transient solutions are possible with both segregated and coupled solvers.

l 1st- and 2nd-order time implicit discretizations (Euler) available for coupled

and segregated solvers.

n Procedure: Iterate to convergence at each time level, then advance in time.

l

2nd order time-explicit discretization also available for coupled-explicit solver.u For segregated solver:

l Time step size, t, is input in Iterate panel.

n t should be small enough to resolvetime dependent features.

l Number of time steps, N, is also required.

n N*t equals total simulated time.

l Generally, use t small enough to ensureconvergence within 20 iterations.

l Note: Use TUI command it # to iterate

further without advancing time step.


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Background: Coupled/Transientl If implicit scheme is selected, twotransient terms are included in discretization.

n Physical-time transient

s Physical-time derivative term is discretized implicitly (1st or 2nd order).

s Time step size, t, defined as with segregated solver.

n Pseudo-time transient

s At each physical-time level, a pseudo-time transient is driven to zero through a

series of inner iterations (dual time stepping).

s Pseudo-time derivative term is discretized:

explicitly in coupled-explicit solver.

implicitly in coupled-implicit solver.

s Courant number defines pseudo-time step size, .

l For explicit time stepping, physical-time derivative isdiscretized explicitly.

n Option only available with coupled-explicit solver

n Physical-time step size is defined by Courant number.

s Same time step size is used throughout domain (global time stepping).

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