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

Fri Jun 23 09:09:57 CDT 2017

Dear Ananias

You say that the coupled Helmholtz solver is used in the case of variable
viscosity because in that case the stress tensor is not diagonal.
Can you provide some reference about the coupled Helmholtz solver, please.

Best,
Andrey

2017-06-07 15:47 GMT+02:00 <nek5000-users at lists.mcs.anl.gov>:

> Hi Vlad,
>
> what you say is correct about the treatment of the viscous term in the
> case of variable
> dynamic viscosity, i.e. the second term in your equation is indeed treated
> explicitly, by
> extrapolating the velocity using previous time steps (the gradient of mu
> is treated implicitly
> though as the dynamic viscosity was already updated to its n+1 value).
>
> The semi-implicit treatment of the full stress tensor in the case of
> variable dynamic
> viscosity is a fairly recent development (2015), which has not been
> published and is not
> described in the 1997/1998 papers or anywhere else in more detail. Note
> that because of
> the implicit treatment of del mu, the inclusion of this explicit term in
> the rhs of the pressure
> equation is not adding a severe diffusion-like CFL restriction to the time
> step (which is
> normally related to second order velocity spatial derivatives , i.e.
> Laplacian).
>
> I don't believe further discussion on this topic is of interest to the
> majority of Nek users,
> so if necessary let's continue any additional conversation off-line.
>
> All the best,
> Ananias
>
> On Wed, Jun 7, 2017 at 5:51 AM, <nek5000-users at lists.mcs.anl.gov> wrote:
>
>> Dear Ananias,
>>
>> thank you for your answer again, but I think, you told about another part
>> of viscous term. In 1997 JSP paper it is clearly explained the situation,
>> when \mu doesn't depend on temperature. But if I, for example, use the  Sutherland's
>> law there is another extra term with (\nabla \mu) and first derivations of
>> velocity as it is shown on the figure below.
>>
>>
>> I saw in the code and it seems like they are treated explicitly in the
>> pressure solver, using the meaning of velocity at n-th time step. Is it so?
>>
>> Best regards,
>> Vlad
>>
>>
>> Среда, 7 июня 2017, 2:43 +07:00 от 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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