Tips and Tricks for Faster Simulation Convergence v6

2011 ANSYS, Inc. April 17, 2014 1

Tips and Tricks for faster simulation convergence

Dr. Valry Morgenthaler ANSYS France

March 2014

2011 ANSYS, Inc. April 17, 2014 2

Introduction

High Performance Computing

Mesh Quality

ANSYS Solvers

Numerical Schemes High order terms relaxation

Reduced Rank Extrapolation

Pseudo Transient Method

PBNS Solver settings for external aerodynamics

Special settings for thermal applications

Convergence Acceleration for stretched mesh

Conclusion

Presentation Plan

2011 ANSYS, Inc. April 17, 2014 3

Introduction

2011 ANSYS, Inc. April 17, 2014 4

Introduction

ANSYS Solver is committed to deliver the best-in-class solvers

These solvers rely on 3 technologies : Hardware

Numerical schemes

Physical models

Time to result can be reduced

Considering a change in physical model is an option

In this presentation we will only talk about how to make the best use of the numerical schemes and hardware

2011 ANSYS, Inc. April 17, 2014 5

High Performance Computing

2011 ANSYS, Inc. April 17, 2014 6

Parallel/HPC in ANSYS Fluids

Every year parallel HPC has always been a major focus on enhanced simulation throughput

The cluster usage increases

GPU usage begins

0

2000

4000

6000

8000

10000

12000

14000

2009 2010 2011 2012 2013

number cores/cluster

0

1

2

3

4

5

6

7

8

9

2009 2010 2011 2012 2013

number cores/processor

0

2

4

6

8

10

12

14

16

18

2009 2010 2011 2012 2013

% of GPU

TOP500.Org

2011 ANSYS, Inc. April 17, 2014 7

Parallel Scalability for large cases

CFX

Up to 90% efficiency over 2048 cores

Fluent

Up to 86% efficiency over 10240 cores

0

100

200

300

400

500

600

700

800

900

0 2048 4096 6144 8192 10240 12288

Rat

ing

Number of Cores

96 Million cells

R15.0

Ideal

0

512

1024

1536

2048

0 512 1024 1536 2048

Wal

l Clo

ck S

pe

ed

up

Number of Cores

150 Million cells

ideal

15.0

14.5

Rating is defined as the number of benchmarks that can be run on a given machine (in sequence) in a 24 hour period. It is computed by dividing the number of seconds in a day by the number of seconds required to run the benchmark. A higher rating means faster performance.

2011 ANSYS, Inc. April 17, 2014 8

Parallel Scalability for small cases

0

5000

10000

15000

20000

25000

0 64 128 192 256 320 384 448 512

Pe

rfo

rman

ce R

atin

g

Num Cores

SEDAN_4M Cells

12.0.19 13.0.1

Processor multicore architecture is also accounted for enabling also a higher parallel scalability for small cases

Fluent

2011 ANSYS, Inc. April 17, 2014 9

Partitioning continuing progress

Partitioning strategies and efficiency is reviewed at each ANSYS release

Compute Node 1 Compute Node 2

P1

P5

P3

P6

P2 P7

P4 P8

P1

P5 P3

P6

P2 P7

P4

P8

Partitioning step finds adjacency amongst partitions; partitions with max adjacency are grouped on same compute nodes

CFX

2011 ANSYS, Inc. April 17, 2014 10

Discrete Phase Particle tracking

More scalable discrete phase particle tracking Over 2x for 512-way parallel

0

1000

2000

3000

4000

5000

6000

7000

16 32 64 128 256 384 512

Rat

ing

246,000 cells, 1 million particles

Hybrid

MPI

2Domain

2011 ANSYS, Inc. April 17, 2014 11

Viewfactor calculation speedup

0.4 million surface clusters

1.1 million surface clusters

R13

R14

CFX

Cluster-to-cluster view factor file writing optimization

Fluent

GPU usage to reduce cluster-to-cluster view factor calculation

2011 ANSYS, Inc. April 17, 2014 12

Parallel File I/O and Startup

The bottleneck of File IO can be leverage using a Parallel File Systems :

PVFS2 (NASA Goddard) Lustre (Linux Cluster) GFS (Google File Sytem)

Case read time reduced significantly at high core counts

Start-up time for 8192-way parallel reduced from 30 minutes to 30 seconds

0

1000

2000

3000

4000

5000

6000

7000

1024 2048 4096 6144 8192 9216 10240

Tim

e in

se

con

ds

150M cell case read time

15.0.0

14.5.0

2011 ANSYS, Inc. April 17, 2014 13

Other Parallel Enhancements

GPUs make their way into the solver :

NVIDIA Tesla 20-series cards NVIDIA Quadro 6000 card

Faster solutions using GPUs Accelerated AMG solver

performance for 3D coupled pressure-based solver cases

2011 ANSYS, Inc. April 17, 2014 14

0

500

1000

1500

2000

2500

3000

3500

4000

0 2048 4096 6144 8192 10240 12288

Rat

ing

NumCores

truck_111m CRAY XE6

13.0.0

14.0.0

15.0.0

Make new architectures available

Support of CRAY XE6 architecture

Support for Intel Many-Integrated-Core architecture

2011 ANSYS, Inc. April 17, 2014 15

Mesh quality

2011 ANSYS, Inc. April 17, 2014 16

Meshing strategy

Accuracy

Simplicity Efficiency

2011 ANSYS, Inc. April 17, 2014 17

Meshing guidelines

Desired mesh quality

What is the maximum skewness and aspect

ratio you can tolerate?

Time available

Faster Tet-dominant mesh vs crafted Hex/hybrid mesh with lower cell

count

Desired cell count

Low cell count for resolving overall flow

features vs High cell count for greater details

Use of non conformal interface !!!

2011 ANSYS, Inc. April 17, 2014 18

Cell not too distorted

Cell not too stretched

Smooth Cells

transition

Mesh quality

Good Not Good

2011 ANSYS, Inc. April 17, 2014 19

Capture flow physics

Grid must be able to capture important physics:

Boundary layers

Heat transfer

Wakes, shock

Flow gradients,

Boundary layers: Velocity and temperature

10-15 elements

Expansion ratios 1.2 1.3

y+ 1 for heat transfer and transition modeling

2011 ANSYS, Inc. April 17, 2014 20

Contours of axial velocity magnitude

Hex mesh Tri mesh

U=0.1

U=1.0

Hex vs Tet mesh

Quad/Hex aligned with the flow are more accurate than Tri

Without dominant flow direction Quad & Tri equivalent

quad t

ri

T = 0

T =

1

U = V = 1.0 , U = V = 1.0 ,

T =

1

U =

V =

1.0

,

U =

V =

1.0

,

T = 0

Contours of temperature for inviscid flow

Accuracy comparison

2011 ANSYS, Inc. April 17, 2014 21

ANSYS Solvers

2011 ANSYS, Inc. April 17, 2014 22

ANSYS Solvers

All ANSYS solver have an all-Mach formulation. Each of these solvers may be more effective on specific

problems Choosing the right solver for the right application is the

first step to a fast simulation convergence ANSYS solvers can be separated in two technologies

depending on which form the continuity equation is solved : Pressure based Navier-Stokes solvers (PBNS) Density based Navier-Stokes solvers (DBNS)

Traditionnaly, PBNS is more suited for incompressible flows and DBNS for compressible

2011 ANSYS, Inc. April 17, 2014 23

Density Based

Pressure Based

ANSYS Solvers

Implicit Segregated

All equations

are solved in a segrageted way

Implicit Coupled

Continuity, Momentum, Energy and Species

are solved in a coupled way

Implicit Coupled

Continuity and Momentum

are solved in coupled way

Explicit Coupled

All equatiions

are solved in a coupled way

Each of these technologies are also separated depending on how equations are coupled together

Fluent Fluent

Fluent Fluent

CFX

2011 ANSYS, Inc. April 17, 2014 24

Density Based

Pressure Based

ANSYS Solvers

Implicit Segregated

Mach < 0.3

Combustion, LES

Implicit Coupled

Mach > 2

Most effective solver

Implicit Coupled

Mach < 2

Most effective solver

Explicit Coupled

Mach > 2

Unsteady flows

Each of these technologies are also separated depending on how equations are coupled together

Fluent Fluent

Fluent Fluent

CFX

2011 ANSYS, Inc. April 17, 2014 25

Pressure-based Solvers

(FLUENT & CFX)

Pressure is used as a primary variable Velocity field is obtained from the

momentum equation Mass conservation (continuity) is achieved

by solving a pressure correction equation Pressure-velocity coupling algorithms are

derived by reformatting the continuity equation

Energy equation (where appropriate) is solved sequentially

Additional scalar equations are solved

in a segregated fashion

PBS solvers can be run implicit only Explicit would be not efficient

Pressure-Based (segregated)

Solve Mass

Continuity;

Update Velocity

Solve U-Momentum

Solve V-Momentum

Solve W-Momentum

Pressure-Based (coupled)

Solve Turbulence Equation(s)

Solve Species

Solve Energy

Solve Other Transport Equations as required

Solve Mass

& Momentum

Pressure-Based

2011 ANSYS, Inc. April 17, 2014 26

Density-based Solvers

(FLUENT)

Density is used as a primary variable the governing equations of continuity,

momentum, and (where appropriate) energy and species transport are solved simultaneously

Additional scalar equations are solved in

a segregated fashion

DBS solvers can be run implicit or explicit

Density-Based (coupled implicit)

Solve Turbulence Equation(s)

Solve Other Transport Equations as required

Solve Mass,

Momentum,

Energy,

Species

Density-Based (coupled explicit)

Solve Mass,

Momentum,

Energy,

Species

Density-Based

2011 ANSYS, Inc. April 17, 2014 27

Numerical Schemes

2011 ANSYS, Inc. April 17, 2014 28

High Order Term Relaxation

2011 ANSYS, Inc. April 17, 2014 29

Higher Order Term Relaxation

Only when high order spatial discretizations are used (higher than first).

Improve calculation startup and behavior of flow simulations

Prevent convergence from stalling in some cases.

This is an effective alternative to starting the solution first order, then switching to second order spatial discretization at a later stage.

Not available with NITA

2011 ANSYS, Inc. April 17, 2014 30

HOTR : Supersonic Jet Impingement

With

Without

Density URF: 0.5

CFL: 2000

Default values for other Solution Controls

No Impact on results

2011 ANSYS, Inc. April 17, 2014 31

HOTR : Supersonic Jet Impingement

Residuals stall at a higher value without HOTR

Solution converged 2.5 times faster with HOTR

With Without

2011 ANSYS, Inc. April 17, 2014 32


2011 ANSYS, Inc. April 17, 2014 33

RRE

Reduced Rank Extrapolation should be used to accelerate convergence of the slowly converging cases

Available as a beta feature since 14.5

It is a vector extrapolation method using the previous convergence steps

Inputs are : The number of steps to use for extrapolation

(ie Subspace size)

The frequency of use of RRE

2011 ANSYS, Inc. April 17, 2014 34

RRE : NACA 0012 airfoil

NACA 0012 at 0 angle of attack

High subsonic case at Mach 0.7

Realizable k-e

Implicit DBNS with CFL=25

RRE is used storing 25 previous solutions

2011 ANSYS, Inc. April 17, 2014 35


2011 ANSYS, Inc. April 17, 2014 36

Pseudo Time Step

Pseudo Time Step is an alternative to solution steering in DBNS

Traditional strategy for steady-state PBNS coupled solver.

with

Pseudo transient method

adding a pseudo transient term to under-relax equation.

with

This under-relaxation method depends on global scales rather than local scales and therefore often converges better on anisotropic meshes

pniinppnpnpp Saaa

1111

11

CFL

p

n

ii

n

pp

n

p

n

p

pp Saat

Vol

11

1

scalevelocity

scalelengtht

_

_

2011 ANSYS, Inc. April 17, 2014 37

The timestep is used to move the solution towards the final answer

Relaxation of the equation non-linearities

Transient evolution of the flow from the initial guess to the steady-state conditions

Converged solution is independent of the timestep used

Initial Guess

50 iterations

100 iterations

150 iterations

Final Solution

Pseudo Timestep

2011 ANSYS, Inc. April 17, 2014 38

Automatic Setup of Pseudo Time Step

CFX

Auto Timescale,

Physical Timescale

Local Timescale Factor (per zone)

Fluent

Automatic

User Defined

2011 ANSYS, Inc. April 17, 2014 39

Timescale is automatically based on a length scale and a velocity scale

Three options are available to set this length scale :

Conservative

Aggressive

Specified or User defined

With the two first methods length scale is based on two easily available length scale :

Volumetric length scale : = 3

Domain length scale : = max , ,

Conservative and Aggressive definition is the same in CFX and Fluent :

Auto Timescale or Automatic Length Scale

Conservative : m(, )

Aggressive : m(, )

2011 ANSYS, Inc. April 17, 2014 40

There is 3 velocity scales which are calculated

Maximum velocity at boundary :

Maximum velocity in the flow field :

Pressure induced velocity : = , ,

Moreover to identify specific physics more variables are computed :

For natural convection Flows : = ( )

For compressible flows : =max(,,)

Auto Timescale or Automatic Velocity scale

2011 ANSYS, Inc. April 17, 2014 41

Timestep is calculated as : = min , , , , ,

For solid zones : =

where =

is the diffusity

Most of the time the Timestep provided is enough

Auto Timescale or Automatic Timescale

0.3

max( , )

0.3

0.1

0.3

max( , , , )

2

2011 ANSYS, Inc. April 17, 2014 42

Often faster convergence than Auto Timescale for appropriate values

CFX

Usually constant but expressions possible, e.g dependent of timestep number

Fluent

Only constant values can be applied

User Timescale

2011 ANSYS, Inc. April 17, 2014 43

Can accelerate convergence when vastly different local velocity scales exist (e.g. jet entering a plenum)

Local Timescale Factor should be used carefully

Conservative value is less than 5

It should not exceed 10-20

Never use for fully converged solution; always finish off with a constant timestep

CFX and Local Timescale Factor (LTF)

2011 ANSYS, Inc. April 17, 2014 44

Transient effect

Sometimes simulations which are run in steady state mode will not converge even with good mesh quality and well selected timestep.

If a steady state run shows oscillatory behavior of the residual plots, a good test is to reduce or increase the timestep by known factors.

If the period of oscillation of the residual plot changes by changing the timestep, then the phenomenon is most likely a numerical effect.

If the period stays the same, then it is probably a transient effect.

In Fluent, switching back to a steady formulation might reduce this problem

2011 ANSYS, Inc. April 17, 2014 45

Pseudo Transient Method Efficiency

Reductions in the number of iterations required for convergence of up to 90% were observed for some cases

CPU time savings are almost directly proportional to the reduction in the number of iterations

Pseudo-transient relaxation study Cases

Courant number coupled: # Iterations

Pseudo-transient coupled: # Iterations

Backward facing step (turbulent: SST)

750 75

Film cooling benchmark (turbulent: SA)

2300 1350

Flat plate, SST transition model 1200 100

Rotor/Stator with the mixing plane model

500 250

Centrifugal pump 220 50 Axial compressor stage 400 110

2011 ANSYS, Inc. April 17, 2014 46

Pseudo time step can be specified with reference to the Navier-Stokes equation time scale :

FlowScalar tTSFt

Pseudo Timestep per equation

CFX

Fluent

pseudo transient can be switch Off per equation under-relaxation panel is then enabled

2011 ANSYS, Inc. April 17, 2014 47


Grid: 7138 quad zones axisymmetric

Solver: pressure based coupled solver

Physical Models: std k-e standard wall functions species transport Premixed combustion

(propane + air)

Mesh at inlet

2011 ANSYS, Inc. April 17, 2014 48

Case PBCS Pseudo Transient off

PBCS Pseudo Transient on

PBCS Pseudo Transient on

But off for Species & Energy

Iter. 244 125 66


2011 ANSYS, Inc. April 17, 2014 49

Initialization

2011 ANSYS, Inc. April 17, 2014 50

Four initialization methods

Standard Hybrid

Full MultiGrid

Previous Calculation

2011 ANSYS, Inc. April 17, 2014 51

Standard initialization

Initialization is done based on specific value Boundary value can both be specified or calculated

from boundary conditions

CFX

Fluent

2011 ANSYS, Inc. April 17, 2014 52

Patch

Patch values for individual variables in certain regions Free jet flows (high velocity for jet) Combustion problems (high temperature

region to initialize reaction)

Cell registers (created by marking the cells in the Adaption panel) can be used for patching values into various regions of the domain.

Multiphase flows (patch different phase volume fractions in one or more regions)

Fluent

2011 ANSYS, Inc. April 17, 2014 53

Hybrid initialization (Fluent)

This provides a quick approximation of the flow field, by a collection of methods.

It solves Laplace's equation to determine the velocity and pressure fields.

This method is more suited with low subsonic flows (Ma < 0.3)

All other variables, such as temperature are automatically patched based on domain averaged values or a particular interpolation method.

2011 ANSYS, Inc. April 17, 2014 54

MFINLET(Primary In) MFR = 1.14; T0 = 322.04 K

POUTLET(Primary Out) P = 0.0

MFINLET(Auxiliary In) MFR = 0.5; T0 = 388.7098 K

POUTLET(Auxiliary Out) P = 0.0

Case Setup : PBNS, SIMPLE Scheme Viscous Laminar, Heat Exchanger - ON LSQ Cell Based, First Order accurate

WALL: Inviscid, Adiabatic

Initialization Fields

FLUENT

Hybrid initialization Example: Multiphase Heat Exchanger

2011 ANSYS, Inc. April 17, 2014 55

Std Init: Iterations = 279 URF

Mom 0.7, Press 0.3, Den 1.0 Energy 0.99

Hybrid Init: Iterations = 102 URF

Mom 0.7, Press 0.3, Den 1.0 Energy 1.0

Hybrid initialization Example: Multiphase Heat Exchanger

2011 ANSYS, Inc. April 17, 2014 56

Full MultiGrid initialization (Fluent)

Can be used to create a better initialization of the flow field FMG Initialization is useful for complex flow problems

involving large pressure and velocity gradients on large meshes

FMG uses the Full Approximation Storage (FAS) Multigrid method to solve the flow problem on a sequence of coarser meshes

Euler equations are solved with first-order accuracy on the coarse-level meshes

To enable FMG initialization, execute the TUI command /solve/init/fmg-initialization

Settings can be accessed by the TUI command /solve/init/set-fmg-initialization

2011 ANSYS, Inc. April 17, 2014 57

Make sure before using FMG you have performed proper standard or hybrid initialization (see previous slides)

Use the FMG verbosity, so you see convergence behavior

Examine the guessed solution from FMG before you proceed with normal iterations.

In general you want to perform more cycles on coarse grids than fine grids

Using too many grid levels can be problematic in some flow topology:

Coarsest level may create single cells in thin passages leading to break up in solution.

Coarse levels not sufficient to resolve hypersonic flow shocks, leading to very bad shock structure straddling the outlines of the agglomerated cells in coarse meshes. Thus we end up with useless initial guess.

FMG tips

2011 ANSYS, Inc. April 17, 2014 58

FMG Example

Numerical solution initialized from the free-stream flowfield

Full multigrid (FMG) initialization applied to obtain the initial solution

FMG initialization is launched by TUI command:

solve/initialize/fmg-initialization

For supersonic and hypersonic flows, it is recommended to reduce FMG Courant number from 0.75 to 0.25:

solve/initialize/set-fmg-initialization

Initial solution after FMGI Final converged solution

2011 ANSYS, Inc. April 17, 2014 59

Previous calculation initialization

A previously calculated solution can be used as an initial condition when changes are made to the case setup

Use solution interpolation to initialize a run (especially useful for starting fine-mesh cases when coarse-mesh solutions are available)

Once the solution is initialized, additional iterations always use the current data set as the starting point

2011 ANSYS, Inc. April 17, 2014 60

Simplified problem initialization

Sometimes solving a simplified version of the problem first will provide a good initial guess for the real problem:

2011 ANSYS, Inc. April 17, 2014 61

Sedan test case

Hybrid mesh (prisms + tetras)

3.9 million cells

3D, steady, double precision

Realizable k-epsilon turbulence model + EWT

Pressure based coupled solver

Pseudo transient parameters Time step Method : Automatic

Lenght scale Method : Conservative

Timescale factor : 1

2011 ANSYS, Inc. April 17, 2014 62

Results comparison Vel Mag

Std init Hyb init

FMG init Interpo init

V max = 213.6m/s

V max = 55 m/s

Velocity field is closer to the end solution for the hybrid init, but the

max speed is quite large

Velocity field is predicted quite well

in both cases

2011 ANSYS, Inc. April 17, 2014 63

Comparison

All theses case have run on the same type of machines and on the same number of procs.

The convergence process, looking at the residual, is identical for the Std and Hyb init. While it is different for the FMG & Ip.

Convergence is reached quicker with FMG and Ip in less than 250 iter while 500 iter is needed for the Hyb & Std.

Initialization Number of iteration to convergence

Standard 600

Hybrid 500

FMG 250

Previous Cal. 150

2011 ANSYS, Inc. April 17, 2014 64

Comparison

The initialization time is clearly much bigger for the FMG init followed by the hyb one.

The time/iter is equivalent for each case.

The RAM required to generate the initialization is increasing with the process

The FMG initialization time is much bigger

sec G

ig

Sec

2011 ANSYS, Inc. April 17, 2014 65

PBNS Solver settings for external aerodynamics

2011 ANSYS, Inc. April 17, 2014 66

Introduction

Switching the pseudo-transient solver option can lead to slower convergence on large cases

The pseudo transient term introduction can trigger the solver sensibility to instabilities

Aerodynamics variables like drag or lift were observed to oscillate in some cases using SST k-w

An alternative approach is to use the classic coupled PBNS solver with F-Cycle for Turbulence, in a two or three steps approach and play on CFL and under relaxation factors (high for Turbulence equations)

Observed Outcome: faster convergence and reduced oscillation of SST k-w

2011 ANSYS, Inc. April 17, 2014 67

CFL and Under-Relaxations in PBNS

Under-relaxation of equations can be implicit and explicit :

Implicit:

= + +

1

Explicit: = +

The CFL number input inside fluent is a way to control all implicit under-relaxation in the resolved equation at the same time

Values of CFL can be chosen in the range of 10-3 to 108 which correspond to a range of 10-3 to 1 for the implicit under-relaxation

=

1 =

1 +

2011 ANSYS, Inc. April 17, 2014 68

Example of improved Solver Settings

Step 1 Step 2 Step 3

CFL 50 200 100

Pressure explicit under relaxation

0.25 0.5 0.25


0.25 0.5 0.25

Turbulence Implicit under relaxation

0.8 0.95 0.95

% of iterations 5 60 35

Step 1 Step 2

CFL 100 200


0.4 0.4


0.4 0.4

Turbulence Implicit under relaxation

0.8 0.95

% of iterations 20 80

3 steps strategy

2 steps strategy

Advanced Solver Settings

2011 ANSYS, Inc. April 17, 2014 69

3 steps vs 2 steps strategy: NACA 4412

Takes about 450 it to fully stabilize forces Takes about 200 iterations to fully stabilize forces

Chord = 299 mm Span width = 150 mm Angle of attack alpha = 13.86 deg. Re ~ 1,000,000 About 3,000,000 cells, hybrid mesh (prism+tets) SST kw

3 steps 2 steps

Default settings: Oscillations!

2011 ANSYS, Inc. April 17, 2014 70

Formula 1 downforce test case

4M cells, hybrid grid

Realizable k-e

SST k-w

SST k-w with 3 step strategy

2011 ANSYS, Inc. April 17, 2014 71

Solver settings for thermal applications

2011 ANSYS, Inc. April 17, 2014 72

Double-Precision Solver

The double-precision solver is designed to minimize truncation error and thus improve the overall heat balance.

Double precision doubles the memory need but only increases by 10% the calculation time

CFX

Fluent

2011 ANSYS, Inc. April 17, 2014 73

Fluent

Using the F-Cycle (or W-Cycle) with reduced termination criterion is preferred

MultiGrid Solver Parameters

Recommended Multi-Grid Cycle Method for cases where diffusion is the predominant effect and for cases with high jump in thermal conductivity.

OR

CFX

Change the solver target reduction scalar might help smoother convergence

2011 ANSYS, Inc. April 17, 2014 74

MultiGrid Solver Parameters influence

F-Cycle Flexible-Cycle

Energy residuals Temperature of engine mount

16.2 Million Underhood case with high jump in thermal conductivity at engine mount

Energy residuals Temperature of engine mount

2011 ANSYS, Inc. April 17, 2014 75

Under-Relaxation of Energy

Under-relaxation of energy equation can be implicit and explicit :

Implicit:

= + +

1

Explicit: = +

Generally if implicit URF is reduced to even slightly (to 0.99), it will take many iterations to converge.

Instead, explicit URF can be reduced to as low as 0.1 and still obtain convergence in reasonable number of iterations.

Fluent

(rpsetvar 'explicit-relaxation? #t)

(rpsetvar 'temperature/explicit-relax 0.2)

(rpsetvar 'temperature/relax 1)

CFX

Change the solver target reduction scalar might help smoother convergence

2011 ANSYS, Inc. April 17, 2014 76

15 million underhood case

Explicit Under-Relaxation

explicit URF=0.5

2011 ANSYS, Inc. April 17, 2014 77

Gradient Schemes

Gradients of solution variables are required in order to evaluate diffusive fluxes, velocity derivatives, and for higher-order discretization schemes.

The gradients of solution can be determined using one of these approaches:

CFX Fluent

Trilinear (default) Green-Gauss Cell-Based (GGCB)

Linear-Linear Green-Gauss Node-Based (GGNB)

Least-Squares Cell-Based (LSCB) (default)

2011 ANSYS, Inc. April 17, 2014 78

Gradient Schemes and conduction

To show the influence of the gradient scheme when a poor quality mesh is used

A simple channel geometry with gas in between two walls

No flow

Gas has a conductivity of 0.1 W.K-1.m-1 for convenience

temperature at 50K

Flux at 9000 W.m-2

Symmetry

=

+

=5.103.9000

0.1+50

= 500

5mm

2011 ANSYS, Inc. April 17, 2014 79

Gradient Schemes and conduction

CFX Fluent GGCB

Fluent GGNB Fluent LSCB

0 K difference

0 K difference

15 K difference

4 K difference

Linear interpolation is always better when the conduction is predominant

2011 ANSYS, Inc. April 17, 2014 80

Secondary Gradients

What is a secondary gradient?

Secondary gradient is introduced when a cell is skewed.

Disable this secondary gradient can help on convergence for poor quality mesh

cT

wT

h

Tfh

TTk

Tkq

cw

n

cT

wT

hr

Perfect Hexahedral Mesh Secondary Gradient = 0

Skewed Tetrahedral Mesh Secondary Gradient

depends on skewness

Secondary gradient

2011 ANSYS, Inc. April 17, 2014 81

Secondary Gradients

How to disable secondary gradients Disabling secondary gradient only adjacent to walls (Alternative wall

formulation)

Disabling secondary gradient only in shell conduction zones

Disabling secondary gradient in all cells, but shell conduction

/solve set expert , yes , , ,

(rpsetvar 'temperature/secondary-gradient? #f)

(rpsetvar 'temperature/shell-secondary-gradient? #f)

2011 ANSYS, Inc. April 17, 2014 82

Secondary Gradients

Do we loose accuracy by ignoring secondary gradient?

Typically, highly skewed cells are located in areas of less importance (unresolved gaps, corners, etc.)

Thus, accuracy is not compromised if proper meshing guidelines are followed.

Default Without Secondary Gradients

2011 ANSYS, Inc. April 17, 2014 83

Secondary Gradients

Ignoring secondary gradient only adjacent to walls improves robustness without any loss of accuracy for cases with highly skewed cells.

LSCB

Q=9,000 W/m^2

50K

T? T(analytic)=9000*.005/.1+50=500K

Error = 42 % Error = 0 %

Alternative Wall Formulation

2011 ANSYS, Inc. April 17, 2014 84

Speed-up conduction convergence for transient Thermal Applications

2011 ANSYS, Inc. April 17, 2014 85

Equivalent thermal behavior

=

=

Equivalent transient behavior if 2 dimensionless quantities are conserved :

Biot number Fourier number

... heat transfer coefficient L ... characteristic length ... solid heat conductance

... solid density cp ... solid specific heat capacity t ... time

2011 ANSYS, Inc. April 17, 2014 86

Speedup Factor

A speedup factor f can be introduced so that :

Assume only cp is varying :

All other variables are conserved

The 2 problems are equivalent

Lets consider the illustrating example of a solid square embedded into cooling airflow

=

=

=

=

2011 ANSYS, Inc. April 17, 2014 87

Solid square cooling example

Initial solid Temperature: 40C

Fluid Temperature: 25C

Speed-up factor of 2, 4, 100, 1000 are tested

constant flow velocity

2011 ANSYS, Inc. April 17, 2014 88

Average Temperature decay :

Simulation time real time

The time step are constant in t*

A smaller number of time-steps are needed for high acceleration factors

Method is valid for quasi stationary flow fields

2011 ANSYS, Inc. April 17, 2014 89

Convergence Acceleration for Stretched Meshes

2011 ANSYS, Inc. April 17, 2014 90

Convergence Acceleration For Stretched Meshes (CASM)

Accelerate the convergence of the DBNS implicit on highly-stretched meshes.

Convergence can be between 2 to 10 times faster than without using CASM.

Use CFL value multiplied by a factor proportional to cell aspect ratio.

Cell stretched perpendicular to flow skipped

Steady-State solution

Can be used with Solution-Steering but Manual schedule adjustment is required.

minl

maxl

minlCFL

A

VCFLt

f

Standard time step

maxlCFLAR

A

VCFLt

f

CASM time step

2011 ANSYS, Inc. April 17, 2014 91

CASM

CASM option can be found in the solver methods description.

When CASM is in use you typically do not need to run the solver at very high CFL value. Range between 2 to 50 is sufficient for most flow cases.

FMG initialization should be used before solving flow with CASM

2011 ANSYS, Inc. April 17, 2014 92

Mach = 0.85, Re = 5e06 , AOA=2.2 deg

Turbulence model SST-k-w

HOTR = On

Mesh properties

3.5 million hex cell mesh

Max AR = 2.6e06

CASM : DPW-4 Wing-Body

10 LBody

2011 ANSYS, Inc. April 17, 2014 93

10 times speed up

Slightly higher drag due to higher numerical diffusion :

CASM : Cd = 0.0283607

Standard : Cd =0.0282161

200 2000

CASM : DPW-4 Wing-Body

2011 ANSYS, Inc. April 17, 2014 94

Conclusion

2011 ANSYS, Inc. April 17, 2014 95

Conclusions

ANSYS CFD is working on the basis of five solvers

Each solver should be used knowing it most favourable domain of application

Multiple now techniques exists to increase solver efficiency : Higher Order Term Relaxation



Convergence Acceleration for Stretched Mesh

Time to convergence can be greatly decreased using these techniques

Tips and Tricks for Faster Simulation Convergence v6

Documents

Transcript of Tips and Tricks for Faster Simulation Convergence v6