[Nek5000-users] Perturbation Mode

[nek5000-users at lists.mcs.anl.gov]

On this topic, here are a couple of observations:

1. Perturbation solver was running slower than the nonlinear
    (std) solver because the perturbation solver did not use
    projection [Fischer1998] to accelerate the pressure solver.

    I've modified this so that pressure projection will be used
    for the perturbation solver if the following conditions are met:

    a. # perturbation modes = 1
    b. baseflow is _not_ computed.

    These conditions could likely be relaxed, but for robustness
    I put them in since I don't have time to test all possible
    combinations at the moment.   The rationale for these restrictions
    is that we (may or) may not want to mix the approximation spaces
    from the different pressure solves that are used to generate the
    initial guesses for each pressure solve.  The above conditions
    ensure that pressure projection is used when there is only a
    single unknown pressure field and thus there will not be cross-
    population of the approximation space.   [ Most likely, it would
    not hurt to have multiple source for the approximation space, but
    things get tricky when there are linear dependencies and my
    discriminators to identify these conditions are not robust.]

2. Linear solver was blowing up while nonlinear was not.

    The case in question is high Reynolds number (minimally dissipative)
    with TORDER=3 --- this case is in fact not guaranteed to be stable
    because the BDF3 timestepper is not A-stable, i.e., there are certain
    regions in the on the imaginary axis that are unstable.  For some
    reason, this issue is cured for the nonlinear case with filtering
    [FischerMullen2001].  It appears, however, that the same fix does
    not cure these linear problems -- not certain why.

    The fix in this case seems to be to switch to TORDER=2, which has
    standard (i.e., CFL type) stability constraints and behavior.

-- Please let me know if you have any further issues with this,
    and thanks to the KTH guys for providing a test case!

Paul


On Mon, 3 Jan 2011, nek5000-users at lists.mcs.anl.gov wrote:

> Hi Neks,
>
> We have been running the perturbation mode in order to study the linear
> evolution of disturbances in a couple of 2D boundary layer cases and are
> now setting up a 3D boundary layer case.
>
> Already for the 2D cases we experienced that the timestep needs to be
> decreased significantly compared to a corresponding nonlinear simulation
> in order to yield a numerically stable simulation. For the nonlinear
> simulations we put the disturbance with a small amplitude on top of the
> baseflow. Hence, running the perturbation mode for the 2D cases was more
> expensive than running a nonlinear simulation but still reasonable.
>
> However, the 3D case seems to become much more expensive. We first ran a
> nonlinear simulation as described above and compared the disturbance
> evolution to results of the parabolised stability equations which
> matched perfectly.
> Running then the perturbation mode for the same disturbance with the
> same base flow did not yield a stable simulation even when the timestep
> was reduced (divided by 5). The disturbance amplitude exploded very
> early. We then took a higher box and increased the resolution which made
> things a little better meaning that the simulation exploded much later.
> However, it is still not stable although the resolution is higher and
> the timestep is much smaller compared to the corresponding nonlinear
> simulation which worked fine. Also, the number of pressure iterations is
> around 20-30 times higher.
>
> Is there any reason why the linear stability equations in nekton should
> behave so much different than the full Navier-Stokes? Are there some
> parameters (filtering etc.) that have to be used differently in this case?
>
> Best regards,
>
> David
>
> -- 
> David Tempelmann
> Linné Flow Center, Mechanics KTH
> SE-100 44, Stockholm, Sweden
> Phone: +46 8 7907161
> E-mail: david at mech.kth.se
>
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