Implicit Time Stepping: First or Second Order?

raz · March 24, 2017, 06:57

Hi all,

I was curious if somebody with more experience on the numerical side of things could enlighten me about the choice of time stepping schemes. I understand that second order will be more accurate but I how important is it when timesteps are already in the order of 10e-5 10e-6?

thanks

LuckyTran · March 26, 2017, 04:08

You really shouldn't use 1st order. Always use 2nd order, or bounded 2nd order. There's really no reason not to use 2nd order. It's only a button click, and memory is cheap nowadays. The smaller your time-step, the more important it is to use a 2nd order time-stepping scheme because this is where the order of the method matters the most.

It really depends on your problem and whether the temporal characteristics is dominated by low of high frequency effects, this determines whether you can get away with 1st order vs 2nd order.

Assuming you are not just having fun and wasting compute hours (i.e. using extremely small time-steps for no reason), I'm guessing that you are using small time-steps because you have a lot of high frequency stuff that you need to resolve. In this case, you need 2nd order or you'll get inaccurate results.

If your problem was mostly low frequency, you could reasonably get away with 1st order as low frequency stuff is less affected by numerical dissipation.

sina_mech · March 27, 2017, 02:40

Quote:

Originally Posted by raz

Hi all,

I was curious if somebody with more experience on the numerical side of things could enlighten me about the choice of time stepping schemes. I understand that second order will be more accurate but I how important is it when timesteps are already in the order of 10e-5 10e-6?

thanks

Bounded 2nd order is a good choice with less oscillations, especially for compressible and/or multiphase problems. Like "LuckyTran" mentioned, I also never noticed a noticeable difference at the computational cost, and it's pretty much like first order!

FIA11 · August 5, 2024, 06:25

How do 1st and 2nd order differ in terms of convergence ?

i am running a transient simulation for fluid flow in elastic tube, and i have been struggling with convergence. I have tried small time step size and more iterations per timestep, yet i always end up with the solution not hitting the convergence criteria until later timesteps.

so i have been contemplating changing my transient method to 2nd order implicit.

March 24, 2017, 06:57	Implicit Time Stepping: First or Second Order?	#1
raz Member Join Date: Nov 2015 Posts: 30 Rep Power: 11	Hi all, I was curious if somebody with more experience on the numerical side of things could enlighten me about the choice of time stepping schemes. I understand that second order will be more accurate but I how important is it when timesteps are already in the order of 10e-5 10e-6? thanks

March 26, 2017, 04:08		#2
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,754 Rep Power: 66	You really shouldn't use 1st order. Always use 2nd order, or bounded 2nd order. There's really no reason not to use 2nd order. It's only a button click, and memory is cheap nowadays. The smaller your time-step, the more important it is to use a 2nd order time-stepping scheme because this is where the order of the method matters the most. It really depends on your problem and whether the temporal characteristics is dominated by low of high frequency effects, this determines whether you can get away with 1st order vs 2nd order. Assuming you are not just having fun and wasting compute hours (i.e. using extremely small time-steps for no reason), I'm guessing that you are using small time-steps because you have a lot of high frequency stuff that you need to resolve. In this case, you need 2nd order or you'll get inaccurate results. If your problem was mostly low frequency, you could reasonably get away with 1st order as low frequency stuff is less affected by numerical dissipation. BlnPhoenix, Tian Li, Aoratos and 1 others like this.

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FIA11 New Member Join Date: Aug 2023 Posts: 4 Rep Power: 3	How do 1st and 2nd order differ in terms of convergence ? i am running a transient simulation for fluid flow in elastic tube, and i have been struggling with convergence. I have tried small time step size and more iterations per timestep, yet i always end up with the solution not hitting the convergence criteria until later timesteps. so i have been contemplating changing my transient method to 2nd order implicit.