Experimental RELAP5-3D Time Step Improvements

Dr. George L Mesina

RELAP5 International Users SeminarNov 18-20, 2008Idaho Falls, ID

Overview

• Background on old method

• Improvements

• Measures

• Results

Background

• RELAP5-3D major time step controls

– Material Courant Limit

– Truncation Error

– Upper and lower time step limits

– Time-targeting

• Must exactly reach plot, output, restart times

– Some other controls via input not relevant

• Trip stop, dump, etc.

Background: Material Courant Limit

• Material Courant Limit (MCL)

• In a control volume:

• Δtin is the time required for fluid to cross from the

entrance to the exit of volume i on time step n.

• Larger time steps with semi-implicit method cause instabilities. Cannot exceed Δti

n in any volume.

• Flow region MCL is:

),max(

),max(ngi

ngi

nfi

nfi

ngi

nfi

ini

vvxt

NVOLitMCL ni ,...1min

Background: Time Step Limits

• Upper and Lower Limits

– The user establishes upper and lower time step limits via input.

– The upper limit creates a minimum number of steps to complete a transient (if Δti

n is never cut).

• Mass Error

– The deviation from perfect solution of the continuity equation.

• The time step is cut if mass error becomes excessive or Δti

n exceeds MCL. . . . Ideally.

Background: Time Step Control

• However, to allow faster code execution, selective violation of MCL was implemented– 5 “bins,” SJ = {Δtn

J+5i | i = 1, 2, . . . , NVOL/5}, J = 1,2,3,4,5

– MCLJ = min(SJ). Note: MCL1 == MCL.

– Δtn = MCL2. Note: Opt 15 sets Δtn = MCL1 = MCL.

• To hit time targets exactly, use halving and doubling.– Plots, minor & major edits, restarts are multiples of DTMAX.

– RULE: Never bypass a target time.

– If we had T=1.75, plot time=2.0, and Δtn = 0.5, the T+dt > 2.0.

• Would need to HALVE Δtn to hit plot time.

• In practice, this is controlled differently.

Background: Time Step Control

• To hit time targets exactly, only double on even time steps. Controlled by integer, NREPET.

• NREPET = Number of Δtn steps needed to reach next multiple of DTMAX.

– Example: Δtn = 0.25*DTMAX, and the cumulative time is: Tn = 5.25*DTMAX, NREPETn = 3.

– Double Δtn implies halve NREPETn. In example, 3/2=1. Wrong!

– Need Δtn+1=0.25*DTMAX. Then Tn+1=5.5*DTMAX, NREPETn+1=2.

– Double now. Δtn+2=0.5*DTMAX. NREPETn+2=1.

Background: Halving & Doubling

• Halving and doubling algorithm based on DTMAX

– Δtn = 2-kDTMAX, 0 < k < log2(DTMAX/DTMIN).

– Halve if MCL or mass error condition violated.

– Double if mass error “low” & Δtn < MCL/2.

• Combining DTMAX limit with selective MCL violation, the flow region MCL is given by:

}2,1{,,...2,1,22

max

JkMCLDTMAXDTMAX

t Jkk

Improvements

• Deficiencies & possible improvements

– Should never violate MCL

• Many users run with exact MCL only.

– Allow time steps other than 2-kDTMAX.

• However, still hit time targets exactly

– Allow code to run above DTMAX (user option).

• Must stay “safely” below MCL.

• Apply multiplier, m<1.0, such that Δtn < m*MCL

Integer Time-step

• All work was done in the context of the integer time-stepping revision of subroutine DTSTEP.– This work enables exact calculation of time in long-running

transients– Important for working with coupled codes.

• To understand integer time-stepping, thing of your computer’s clock cycle.– If it is a 4 GHz machine, it performs 4,000,000,000 ticks per

second.– Each tick is 1/4000000000 sec.– An integer, t, can count the ticks from 1 to 4000000000.– Floating point time T = t/4000000000.0

Time Targets

• A 4-step approach is used to hit time targets.

– Check for target 3 steps in advance.

reachedtargetTime,

stepremainingOne,

stepsremainingTwo,2

stepsremainingThree,3,mod3

saved

edit

edit

editedit

tt

ttt

ttt

tttt

t

Approach MCL if above DTMAX

• DTMAX is often far below MCL

• If the user could allow violation of DTMAX, larger time steps could often be taken.

– Propose making the option controlled on the time step card.

– The user could turn it on and off to examine important parts of the transient as needed.

MCL vs Current Time-step (DTMAX)

• Typpwr

Typpwr Violating DTMAX

•

Selecting the MCL Multiplier, m

• Multiplying the MCL by safety value ensures the time step does not come “too close” to instability.

• A study was done by running numerous test models with a variety of values of m.

– m = 0.5k, k = 1, 2, . . . , 20.

– The input models were taken from the set of problems transmitted with the code.

• The study showed that generally, .85 <= m <= .95 was best.

– In fact, m = 0.9 proved about the best choice.

Background

• b

Background

• b

Combining DTMAX violation and m

• Combined improvements

– Sometimes the number of time steps is reduced significantly.

– Sometimes there is no change.

• Note that use of excessively frequent time targets interferes with every improvement

– Because code must reduce time step to hit target

• For Typical PWR, the reduction is most pronounced.

End

• end

Conclusions

• The existing algorithm for semi-implicit time-stepping was reviewed.

• Several improvements were suggested.

• Two improvements were combined and shown to allow significant reduction in code runtime

• These are the MCL multiplier and DTMAX violation

• It is proposed that these be made a user option.