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phi -= pEqn.flux() vs. linearInterpolate(U) & mesh.Sf() - Page 2 -- CFD Online Discussion Forums

After re-reading your last and previous posts and also Issa's paper and Jasak's Thesis, I think I should clarify this a bit. My previous consideration is NOT right, since H(U) is updated between every two consecutive PISO correctors (so k-1 times along the whole time step, if k is the number of PISO correctors), but ONLY in terms of the cell-centered neighbour velocities U_N, and NOT in terms of the phi contribution inside discretization coefficients (a_N, but also the owner coefficient a_P, which contributes in the construction of the HbyA vector).
algorithm  piso  cfd  programming  ofm 
november 2018 by aries1988
phi -= pEqn.flux() vs. linearInterpolate(U) & mesh.Sf() -- CFD Online Discussion Forums

Now lets take a look into the PISO algo itself. I will not cite the code but it should be easy to follow.
1) create the UEqn using the last- known phi. Note that any "XEqn" is like a black box, with a void space for the unknown. The imporatant stuff are the coeffs.
2) if you like, solve momentum predictor (this is unnecessary and can be dropped for time saving).
3) extract the semi-central coeffs from the UEqn, reverse them and call rAU. This is the famous "operator splitting".
4) pressure loop:
4.1) recalculate velocity: U = rAU * H();
4.2) recalculate fluxes: phi = interpolate(U) * S; note that the flux field is NOT divergence free;
4.3) solve for pressure using the non divergence free flux
4.4) solve it several times...
5) now, we solved for pressure with non-div-free phi. But the literature (Jasak's thesis, Issa et al.) tells us, that we can correct the fluxes using the pressure field and this way ensure div-free condition. This is the famous phi -= pEqn.flux();
6) Finally, we correct the velocity field, acquiring a good approximation of the velocity field.
algorithm  cfd 
november 2018 by aries1988
OpenFOAM guide/The SIMPLE algorithm in OpenFOAM - OpenFOAMWiki
The SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) allows to couple the Navier-Stokes equations with an iterative procedure, which can be summed up as follows:

Set the boundary conditions.
Solve the discretized momentum equation to compute the intermediate velocity field.
Compute the mass fluxes at the cells faces.
Solve the pressure equation and apply under-relaxation.
Correct the mass fluxes at the cell faces.
Correct the velocities on the basis of the new pressure field.
Update the boundary conditions.
Repeat till convergence.
The steps 4 and 5 can be repeated for a prescribed number of time to correct for non-orthogonality.
algorithm  cfd  explained 
november 2018 by aries1988
IcoFoam - OpenFOAMWiki
A highly annotated version of the code is shown below. Ferziger and Peric, below, give a fairly standard overview of PISO, but OpenFOAM uses a notation and form closer to Jasak and Rusche's theses. References to PISO documentation are:
explained  cfd  algorithm 
november 2018 by aries1988
Access to neighbor faces on a boundary -- CFD Online Discussion Forums
For the moment I solved the problem in a more simple way. I perform a double interpolation:
- interpolation of the face values to obtain the values on the boundary points (faceToPointInterpolate).
- interpolation of the boundary values to obtain the values on the face centers (pointToFaceInterpolate).
mesh  algorithm 
november 2018 by aries1988
Is the Algorithmification of the Human Experience a Good Thing?
Skeptics will point out that those algorithms are designed by corporations to serve their interests, not yours. Social media companies, for instance, want to keep you on their services as long as possible, which makes them prone to pushing emotionally charged content that might not be super healthy for you or for society. And even a benevolent algorithm can produce negative or unwanted results.

The video wasn’t directly crafted by a machine. But it wasn’t totally a human creation, either. Rather, it was optimized to appeal to YouTube’s content algorithm, which automatically plays related videos one after the other. “Johny Johny Yes Papa” copies enough elements of popular kid’s videos — a certain length, musical beat, color palette and visual style, along with key words and lyrics — that YouTube’s algorithm will line it up after more popular songs.

At least on a symbolic level, there is something unsettling about a global, faceless content empire that hoovers up human culture and processes it into homogenized nothingness to be fed to kids via tireless social media algorithms that seek, above all else, to maximize time spent on site.
society  engineering  crisis  question  future  children  video  ai  algorithm 
september 2018 by aries1988
[Groupe Calcul] : Atelier "initiation à PETSc"
Le Groupe Calcul et la Maison de la Simulation ont proposé, dans le cadre du projet Equip@meso, une formation d’initiation à la librairie PETSc du lundi 18 mars au mercredi 20 mars 2013. Cette formation aura lieu à la Maison de la Simulation. Le programme complet est disponible ici :

Les intervenants sont Jérémy Foulon, Loïc Gouarin et Serge Van Criekingen.

L’organisation de cette formation, en collaboration avec le réseau LyonCalcul est à nouveau prévue (par les mêmes intervenants) sur le campus de la Doua, à Villeurbanne/Lyon.
Toutes les informations sont en ligne :
resource  hpc  algorithm  algebra 
july 2017 by aries1988
There’s a big problem with AI: even its creators can’t explain how it works

In 2015, researchers at Google modified a deep-learning-based image recognition algorithm so that instead of spotting objects in photos, it would generate or modify them. By effectively running the algorithm in reverse, they could discover the features the program uses to recognize, say, a bird or building. The resulting images, produced by a project known as Deep Dream, showed grotesque, alien-like animals emerging from clouds and plants, and hallucinatory pagodas blooming across forests and mountain ranges.
ai  health  medical  cancer  problem  communication  today  human  google  art  visualization  algorithm 
april 2017 by aries1988
Generating naming languages

First off, the majority of words in Mandarin have two syllables. This gives it a very clear rhythmic quality. Secondly, the syllable structure is pretty much constant. Each syllable consists of a single consonant, a vowel or two, and then optionally either /n/ or /ŋ/ (written ng). So 'shan' is a valid Mandarin syllable, but 'stan' and 'nash' are not.

In real languages, words are built out of units called 'morphemes', which are the smallest units of language which still carry meaning. Some words are single morphemes (e.g. 'happy', 'sad', 'platypus'), and some can be divided up into smaller units (e.g. 'un-help-ful', 'rest-less', 're-consider-s'). The relationship between syllables and morphemes, both of which combine to form words, is hazy at best.

Fortunately, we're making up our language, so we can make it as simple as we like. One syllable equals one morpheme.
game  language  invention  howto  comparison  primer  python  map  algorithm 
january 2017 by aries1988

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