Experimental RELAP5-3D Time Step Improvements

1. Experimental RELAP5-3D Time Step Improvements Dr. George L Mesina RELAP5 International Users Seminar Nov 18-20, 2008 Idaho Falls, ID

2. Overview • Background on old method • Improvements • Measures • Results

3. 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.

4. 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 Δtin in any volume. • Flow region MCL is:

5. 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 Δtin 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 Δtin exceeds MCL. . . . Ideally.

6. Background: Time Step Control • However, to allow faster code execution, selective violation of MCL was implemented • 5 “bins,” SJ = {ΔtnJ+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.

7. 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.

8. 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:

9. 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

10. 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

11. Time Targets • A 4-step approach is used to hit time targets. • Check for target 3 steps in advance.

12. 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.

13. MCL vs Current Time-step (DTMAX) • Typpwr

14. Typpwr Violating DTMAX

15. 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.

16. Background • b

17. Background • b

18. 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.

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20. 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.