On perspectives for common research in the Leibniz MMS network in the field of Computational and Geophysical Fluid Dynamics
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| Anzahl der Teile | 22 | |
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| Lizenz | CC-Namensnennung 3.0 Deutschland: Sie dürfen das Werk bzw. den Inhalt zu jedem legalen Zweck nutzen, verändern und in unveränderter oder veränderter Form vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen. | |
| Identifikatoren | 10.5446/21912 (DOI) | |
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| Produktionsjahr | 2017 | |
| Produktionsort | Hannover |
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00:00
PerspektiveRechnernetzNumerische StrömungssimulationVorgehensmodellMereologieNumerische StrömungssimulationSchreib-Lese-KopfPerspektiveMultiplikationsoperatorDatenfeldKategorie <Mathematik>Angewandte MathematikEreignishorizontRichardson, Lewis FrySoft ComputingPhysikalismusEndliche ModelltheorieFluidVorhersagbarkeitWissenschaftliches RechnenProzess <Informatik>Vorlesung/KonferenzComputeranimation
01:29
KontrollstrukturOrtsoperatorPunktwolkeWellenlehrePhysikalismusZirkulation <Strömungsmechanik>AbstandZentrische Streckung
02:13
OrdnungsbegriffDissipationProzess <Informatik>EnergiedichteUmkehrung <Mathematik>Turbulente StrömungKorrelationNichtlineares GleichungssystemKinetische GastheorieDichte <Physik>Stokes-IntegralsatzLokales MinimumReynolds-ZahlNumerische StrömungssimulationVektorpotenzialDruckverlaufSimulationMetrisches SystemDatenverwaltungData DictionarySoftwareKnotenpunktSystemplattformCloud ComputingMathematikSpannweite <Stochastik>WinkelSystemprogrammierungAerothermodynamikDatenstrukturDatenmodellWiderspruchsfreiheitRuhmasseATMElektronischer ProgrammführerErhaltungssatzDiskrete UntergruppePlancksches WirkungsquantumTheoretische PhysikVorgehensmodellMultiplikationRechenwerkMarketinginformationssystemCase-ModdingDampfPartielle DifferentiationKategorie <Mathematik>SkalarfeldVerhandlungs-InformationssystemKanal <Bildverarbeitung>Produkt <Mathematik>Funktion <Mathematik>KreisringMereologieDesintegration <Mathematik>Symmetrische MatrixBitrateScherbeanspruchungGradientSechseckNeuronales NetzBenutzerfreundlichkeitGruppenkeimMehragentensystemInstantiierungDatenflussProzess <Informatik>Zentrische StreckungSummengleichungExpertensystemVollständiger VerbandGrößenordnungDiskrete UntergruppeGeschwindigkeitDifferentialSchlussregelNumerische StrömungssimulationEinfügungsdämpfungReibungswärmeTensorImpulsFluss <Mathematik>AnalysisInteraktives FernsehenAbstimmung <Frequenz>DruckverlaufDatenverarbeitungssystemVerdunstungWasserdampftafelKugelZusammengesetzte VerteilungFlächentheorieAbstandDistributionenraumGradientDerivation <Algebra>Shape <Informatik>AerothermodynamikSechseckGesetz <Physik>WiderspruchsfreiheitZweiQuaderPunktWellenlehreNummernsystemMultiplikationsoperatorKollaboration <Informatik>LogarithmusMathematikerinTermFormale SpracheBitForcingSpeicherabzugComputersimulationMaschinenschreibenNichtlineares GleichungssystemBasis <Mathematik>Endliche ModelltheorieDissipationStatistische HypotheseCoxeter-GruppeSystemplattformHilfesystemMereologieSpannweite <Stochastik>SoftwareFluidDichte <Physik>DatenfeldEnergiedichteTurbulente StrömungDomain <Netzwerk>BitrateDigitale PhotographieMathematikKnotenpunktDifferenteDatenstrukturEinfach zusammenhängender RaumLuenberger-BeobachterNichtlinearer OperatorStrömungsrichtungMathematisches ModellKinetische EnergieGrenzschichtablösungStreaming <Kommunikationstechnik>RandwertKardinalzahlWirbelströmungInnere EnergieStruktur <Mathematik>Kategorie <Mathematik>KonzentrizitätProdukt <Mathematik>Treiber <Programm>Jensen-MaßPunktwolkeRichtungVorhersagbarkeitDampfRadiusKontrollstrukturTeilbarkeitÄhnlichkeitsgeometriePhasenumwandlungComputervirusDruckspannungIdeal <Mathematik>Ordnung <Mathematik>Physikalisches SystemDatensatzSelbst organisierendes SystemUngelöstes ProblemBildschirmmaskeSchnittmengeComputerspielLesezeichen <Internet>RechenwerkMAPCASE <Informatik>PhysikerAusdruck <Logik>TelekommunikationTypentheorieMusterspracheFlüssiger ZustandDatenkompressionKontrollflussdiagrammWald <Graphentheorie>StellenringMetropolitan area networkLeistung <Physik>BruchrechnungQuellcodeGenerator <Informatik>Computeranimation
Transkript: Englisch(automatisch erzeugt)
00:00
Hello everybody. This is the first talk in this workshop. My topic is on the perspective of Coleman Research in the Leibniz MMS workshop in the fields of computational fluid dynamics. So my talk will be about computational fluid dynamics and it will also summarize what we have done in the last half year
00:24
after the last mini workshop at the Weierstrass Institute in Berlin in the field of computational fluid dynamics. So perhaps I'm from the Institute of Atmospheric Physics and atmospheric physics was one of the first applications of mathematical modeling
00:44
especially computational fluid dynamics because in 1922 Lewis Fry Richardson wrote this book on weather prediction by numerical process. And this was somehow the kick off of scientific computing at least in our field.
01:03
And you can see here how he imagined in the time before there were computers how to compute the weather. So computers at his time were human beings having a pencil in their hands and he thought about 64,000 people computing the weather.
01:24
So you can read this in this book if you are interested in. So our research at the Institute of Atmospheric Physics in Külungsborn covers the global circulation of the atmosphere up to heights of about 100 kilometers.
01:45
And in these heights which is the upper mesosphere lower thermosphere you can see these kind of noctilucent clouds. And these are formed by waves which travel from the troposphere through the stratosphere into the mesosphere and break at this position.
02:06
So this is a very large scale problem because the waves travel a long distance from the troposphere and to the mesosphere. But then they break and this is quite a small scale process.
02:20
This is a picture from the troposphere surely but you cannot have a photograph which looks from the side on this breaking process. And we are measuring, besides computing we are also measuring what is happening in the mesosphere. And so for instance we have rocket flights which measure the dissipation rates
02:46
and we have also LIDAR observations which can measure the distribution of the temperature. As you can see on the left side. And our goal is to simulate all these processes from the largest scale until the finest scales.
03:07
And here you can see a sketch of typical modeling at our institutions. So we have a global model which you can see on the, on this for instance here. And you see large scale structures which are for instance Rossby waves which you can see here.
03:23
And they break by doing these filaments in the vorticity field. And then if you go, this is at the upper part of the troposphere. And here if you go higher up for instance in the mesosphere you can see these waves which were, which you can see as the noctilutin clouds.
03:44
And these are immediate scale features. And then you have to simulate how they break. And you, and the way how the atmosphere dissipates the energy depends on the
04:01
small dissipative processes which happen here on the grid scale of our numerical model. So that means we are dealing with all kinds of orders of magnitude in the kinetic energy density. So you have these large scales here, you have the intermediate scales here.
04:23
And then you have the dissipation scale here. And clearly it is very difficult to have all these processes in one model and in one viewpoint. And similar problems are also to be seen at other institutes.
04:45
Not only the IRP has these kind of modeling but also other institutes like the IOV, the Weierstrass Institute or the TROPOS Institute. They are doing this kind of computational fluid dynamics on either atmospheric or oceanic flows.
05:02
And they are all faced with this whole range of orders of magnitude. So for instance the Weierstrass Institute is interested in how to model geostrophic balance. This is also very important for my own modeling. If you want to have, to simulate the whole atmosphere you have to keep the geostrophic balance.
05:29
So this is the first dominating balance in the atmosphere, you have to keep it right. Then on this intermediate scale a lot of institutes are faced with turbulence modeling.
05:45
This is especially for instance also the TROPOS and also the IOV, the Institute of Osse-Forschung. But also some agricultural institutes which compute heat fluxes in animal bonds for instance.
06:02
Which is a small scale process but still very turbulent and very important. And then on this very small scale end where you have dissipation, your thermodynamic consistency is a very important topic. Because it says how energy is actually dissipating.
06:23
So if you are consistent with the second law of thermodynamics you know that all your energy is really dissipated and not created out of nothing. And then we have the institutions which are dealing with all kinds of orders of magnitude.
06:41
For instance the Potsam Institute for Klima-Folgenforschung which adds to this spatial scale also a very large temporal scale. So and this is what we realized in our last MMS mini workshop. And because these topics were so diverse we had to first find a common language.
07:05
And we have to first be aware that everybody of us has a different history, background and culture. And if a mathematician talks about a wave it's not the same as a meteorologist talks about a wave. And therefore we have to be aware of our diverse backgrounds.
07:23
But we have to acknowledge that this diversification really takes place. And therefore we have to somehow organize our knowledge and organize our methods and organize our software. I think this is a very important topic for the future.
07:41
This was what we discussed first and then we defined some goals for collaboration in this MMS mini workshop. And we thought about how to organize collaboration between the institutes which are dealing with computational fluid dynamics. We thought that it would be good to have one institution as a junction point which would be the Weierstrass Institute.
08:05
So it keeps in touch with applied mathematics and it can go into some depths where other institutions cannot go into. And we decided that it could be a good idea to have a core supervision of bachelor or doctoral thesis or master thesis.
08:23
And the wires could help in sharpening mathematical part of the proposals and help in solving mathematical problems. And clearly we should continue with all the summer schools or mini workshops or whatever kinds of exchange platforms.
08:44
So and this is what has been established since the last mini workshop. Which we could define existing or ongoing collaboration between diverse institutions of the Leibniz domain shaft.
09:00
So we have the Weierstrass Institute here somehow in the center and we have other institutions. And we could say that there are already common interests or at least collaborations going on. So for instance with the agriculture institute, I don't know exactly how it, was this ATB in a while?
09:23
Okay. The second one is Technic. Yeah, Technic, agriculture Technic. It is Borneam or it is Aspergine. Ah, Borneam, okay. Agriculture Technic. Borneam, yeah. So there is a collaboration between the TROPOS and ATB about turbulentine fluxes, boundary conditions and these flows in animal bonds for instance.
09:44
Then there is a common interest between the Weierstrass Institute and the TROPOS Institute in modeling on prismatic grids. Then between the Institute of Atmospheric Physics and the Weierstrass Institute is the thinking about structure preserving modeling and improving of accuracy of operators.
10:01
And then there is a long connection between the Institute of Osseforschung and the Institute of Atmospheric Physics about turbulence modeling. And this is because we are so close together. So Wannemünde is about 30 kilometers away from Kildungsborn. And then we have other ongoing collaborations, for instance with the Institut für Kristalltschwichtung und the Weierstrass Institute.
10:25
So there is support for solutions of technical problems from the Weierstrass Institute for either the Institut für Kristalltschwichtung or the Institut für High Performance Electronics.
10:41
And then there is also a collaboration between Weierstrass Institute and Geophysical Research that there is a help for the geophysicists in sharpening mathematical aspects in research proposals.
11:00
So there is a lot of collaboration already ongoing. So our network is not only on a sheet of paper, so we are really doing something. And for proving that this is really the case, I want to focus on some special topics which are really, or which are really interesting for several partners in CFD and GFD.
11:27
So for instance the topic of thermodynamic consistent modeling, I will shortly show an example. An example and robust structure preserving method that avoid unphysically numerical induced instabilities and
11:44
turbulence modeling, which is a topic which every CFD, GFD modeler is interested in. And most of these topics can, or most of the topics we are doing research on can
12:01
take at least one of the three properties of a numerical scheme, namely consistency, accuracy and efficiency. And some institutions want to be more efficient, others want to be more accurate. And other institutes say whether it's consistent or not doesn't matter, for the short time scales I'm interested in consistency is not so important.
12:29
So these are the main topics. And here is an example, for instance, of common interests between, or common interests of completely different, from completely different backgrounds.
12:44
For instance, at the last mini workshop Wolfgang Dreyer presented an example in electrochemistry, which was, which deals with the flow of an electrolyte in a battery and how the ions are moving forth and back and how they are diffused.
13:04
And there was a problem that some thermodynamic consistency was not met in the old model which was set up by Nernst and Planck. And in this old model, the concentration of some ions alpha was, besides the electric potential, the only driver of this flux.
13:35
And this inconsistency was, or it was said that the inconsistency in thermodynamics
13:46
was caused by the fact that the barycentric velocities were not correctly computed. And that the different pressures of the constituents in the electrolyte was not taken into account.
14:02
And therefore the interaction between the different ions were not captured correctly. And if one goes into the analysis with more consistency and more stringent thinking, one comes up with a new flux formulation here, which especially adds here a pressure gradient term.
14:24
And one can see that the distribution of the different ions is, or that the distribution of ions here as a distance from one of the anode or cathode, I don't know, differs in the old model from the new model.
14:44
And why do I bring this example? Because in meteorology and in meteorological modeling we have a very, very similar problem. And it can be traced back to a similar deficiency in the old viewpoint.
15:03
For instance, we are usually, we are dealing with a mixture of dry air and water vapor. And so, for instance, for the evaporation from the ground, you bring up water vapor in the atmosphere and it will be diffused. And in the conventional setting, you say that this water vapor flux is just given by the gradient of the specific humidity.
15:26
And then, in a similar way as the example with the anions and cations, you have dry air and water vapor, which is a mixture in the same way.
15:40
And also our problem was that we had some inconsistency in the derivation of the equations. And finally, we got a new formula, which differs from the old formula, especially by a term which goes also with the gradient of the pressure.
16:02
If you say that the logarithm of rho times t is proportional to the pressure. So, we have this pressure gradient was added in the new viewpoint for the electrochemistry example.
16:21
And in a similar way, this was added in the meteorological example where you have dry air and water vapor. And also in this, in our example, you see that the old solution is a bit different from the new solution.
16:42
In the new solution, you have a bit more enhanced upward water vapor flux. So, this was one example where we can see that from totally different topics, we have common problems. And now we have, we changed the topic and we come to the problem of atmosphere and ocean modeling on the basis of the Navier-Stokes equation.
17:09
So, we have dry air and no water vapor and we have also incompressibility. And then I learned from Alexander Linke that in usual solvers for the Navier-Stokes equations, the balance
17:30
between the pressure gradient and between a force which could be here the Coriolis force is not well represented. And that if one represents, if one takes an account that most of this force is balanced by a
17:50
gradient, then one can find that the geostrophic balance is dominating the whole momentum equation of the Navier-Stokes equation.
18:07
And that large parts of the pressure gradient is balanced by the Coriolis force but only large parts. So, the background, so and now the usual or classical solvers of
18:24
the Navier-Stokes equation are not able to correctly simulate this geostrophic balance. And therefore, lead to solutions which are completely unrealistic. I will shortly explain what these solutions are.
18:43
You all know that we have large ocean basins, for instance the Atlantic basin and that the Gulf current is going on the western coast of this Atlantic basin.
19:02
And the most simple mathematical model for this, that the Gulf stream is only on the western side, is the so-called Stommel gyre, which is, this is a typical oceanographic problem.
19:23
And the correct solution looks like this, so you have most flow goes on the western coast. With the classical solution of the Navier-Stokes equations, you would not see that most of this current is going on the west coast. And this, and the background is that this geostrophic balance is not correctly simulated.
19:43
And if you would go into the detail and for instance derive the discrete vorticity equation, you would also quickly see where the problem is coming from. This is one example where we want to launch in a collaboration.
20:02
And then we have a second example which we are already working on and we had a meeting on this was that I had a problem which I could not solve. And I could ask some expert from the Weierstrass Institute to help me along with this.
20:22
And the problem here is that I want to simulate a correct momentum diffusion tensor which works as a friction for the velocity.
20:40
And it introduces a frictional heating, so this is a loss in the kinetic energy and will be again in the internal energy. And this structural, this mathematical structure of a product rule of differentiation should be preserved during the discretization.
21:08
And we are working on how to discretize these deformations E and F on a hexagonal based grid.
21:21
And the problem we are stumbling in is that on deformed grids like to be seen here, our deformations which occur in this tensor are not accurate enough. And our outcome of our first meeting in January was that we improved the accuracy
21:43
of these deformations by reconstructing directional gradients via a polynomial reconstruction as you can see here. So and the background of the whole stuff is that on the sphere it is very, it is
22:02
of importance to have a good coverage of the surface of the sphere with grid points or grid boxes. And so hexagonal shaped grid boxes are very fortunate and we have a model which works on hexagons on a sphere and this is how we predict the weather.
22:35
And okay, let's now come to the summary. So we have implemented a mini
22:43
-workshop on CFD and GFD in last September and we have also created some collaborations. For instance, as already shown, we have now, we want to develop a pressure robust scheme for the sphere which
23:04
means that we want to keep the geostrophic balance well defined and this should also be developed for compressible flows. And we are working together in improving the accuracy of the momentum diffusion tensor and
23:23
then we have this example with the heat fluxes and boundary conditions in animal bonds. So Oswald Knodt and somebody from the Agriculture Institute are working together to solve the problem with the animal bonds. And then we have also a collaboration which resulted in a draft proposal on simulations for geothermal
23:48
energy and is submitted to BMBF and this was a collaboration between the LIAC and the Weierstrass Institute. So we want now to continue the MMS days and in the present workshop or tomorrow we will have mini-workshops also on
24:09
CFD and GFD and I think this will be a good idea to further promote interdisciplinary exchange and collaboration within the Leibniz Institute.
24:22
Thank you very much.
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