[Nek5000-users] Nek5000 documentation details: Pn-Pn pressure solver

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

Dear Vlad,

this is correct, the coupled Helmholtz solve is used in the case of the
full stress tensor
because in that case the stress tensor is not diagonal.

The splitting approach is based on an irrotational-solenoidal decomposition
of the velocity
(which is described in the 1997 JSC paper); the divergence of the former,
which appears in
the rhs of the pressure equation is treated implicitly (it is zero in the
case of constant viscosity
and incompressible flow), whereas the divergence of the latter is treated
explicitly through the
vorticity (which also appears in the pressure rhs and the pressure BC and
is again zero in the
case of constant viscosity and incompressible flow; this is not the case in
the pressure BC) .

It was proved in the JSC and JCP papers that this splitting approach, which
allows for an
uncoupled solution of the pressure and velocity equations, leads to a
high-order overall
accuracy in time.

Best,
Ananias

On Tue, Jun 6, 2017 at 7:09 PM, <nek5000-users at lists.mcs.anl.gov> wrote:

> Dear Ananias,
>
> thank you for a prompt and clear response! About the coupled Helmholtz
> solver, it is used to solve for three velocity components at once. Is it
> due to \nabla \mu^{n+1} \nabla v^{n+1} term? Thus, in the equation for v_x,
> for example, there are terms with derivatives of v_y and v_z, since they
> are at n+1 time step, they should go to the matrix, and not to the RHS of
> the equation.. Right?
>
> The second issue is that the same term with additional \nabla appears in
> the equation for Laplacian p^{n+1}. Do you treat it explicitly here? I mean
> at the time step n instead of n+1?
>
> Is there no conflict between implicit treatment of viscous terms at the
> `velocity' step while doing it explicitly during `pressure' step?
>
> Best regards,
> Vlad
>
>
>
> Вторник, 6 июня 2017, 17:51 +07:00 от nek5000-users at lists.mcs.anl.gov:
>
>
> Dear Vlad,
> the low Mach Pn-Pn approach is based on the 1997 (JSC) and 1997 (JCP)
> papers you mention and it consists of 3 steps as you describe, i.e.:
> a) first the velocity is updated using the extrapolated convective term,
> b) then the Laplacian of pressure is calculated due to convection, after
> that
> c) the velocity is updated using the pressure gradient and accounts for
> viscous term
> The coupled Helmholtz solver is used for the velocities only when using
> ifstrs=true, that
> is when you want to include the full stress tensor. Otherwise, it is using
> separate Helmholtz solves for each of the velocity components, similar to
> Pn-Pn-2.
> Hope this helps clarify things.
> All the best,
> Ananias
>
>
> On Tue, Jun 6, 2017 at 7:29 AM, <nek5000-users at lists.mcs.anl.gov> wrote:
>
> Dear Neks,
>
> reading the documentation I got the impression that Pn-Pn solver (low
> Mach) first solves the pressure where the convective and viscous (!) terms
> are taken into account. After that using this p^{n+1} we solve for velocity
> field. It seems that the algorithm consists of only 2 steps (pressure +
> velocity).
>
> However, reading the paper by Tomboulides, Lee, Orszag (1996) which is
> referenced inside the code, I see the projection algorithm where first the
> velocity is updated using the extrapolated convective term, then the
> Laplacian of pressure is calculated due to convection, after that the
> velocity is updated using convection and pressure gradient. The last step
> accounts for viscous term.
>
> I am a bit confused, could you please help me out here? Which method is
> used?
>
> PS. Another thing is the coupled Helmholtz solver in Pn-Pn. I see that in
> case of Pn-Pn-2 each velocity component is treated separately (segregated
> solver). However, this coupled thing slightly confuses me, why not treating
> it separately as in Pn-Pn-2? Could you please comment there as well? Thank
> you.
>
> Best regards,
> Vlad
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