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On perspectives for common research in the Leibniz MMS network in the field of Computational and Geophysical Fluid Dynamics

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and everybody in this as in the 1st part
in this workshop on my topic as on perspective of common research and indictments and then as the workshop in in the fields of computational fluid dynamics of my talk will be about computational fluid enemies and it also summarized so what we have done in the last few years after the last many workshop at of Irish has Institute in new in the field of computational fluid dynamics so perhaps
as a I'm from there at the Institute of Atmospheric Physics and atmospheric physics was 1 of the 1st applications of mathematical modelling especially computational fluid dynamics because in the 19 22 Lewis Fry Richardson wrote this book on the matter Prediction by Numerical Process and and this was some the kick off of scientific computing at least an of field and you can see here as how in he imagined in the time before the via computers how to compute event so computers at his time where human beings having a pencil in their head and their hands and he thought about 64 thousand people computing the weather so you can read this and this book if you're interested in so in our
research and institute as at of atmospheric physics in couldn't born and covers the global circulation of the atmosphere up to a height of about 100 kilometres and these heights such as the measles fearless Wilson was here you can see these kind of but not to Newton knocked news and clouds and these are formed as by waves which travel from the troposphere sodas stratosphere into the museum break at this position so this is a very large scale of a problem because the waves travel a long distance from the troposphere and 2 and measles here but then
they break and this is a quite a small scale process and this is a picture from the troposphere initially but did you cannot have a photograph which looks from this side and this breaking process and so we have measure of
besides computing the also measuring what is happening in the in the in the mesosphere and so effective for instance we have rocket flights which was a minute which measure the dissipation rates and and we have also lighter observations which can measure the distribution of the temperature 2nd see on the left side but and our goal is to simulate all these processes from the larger scale and the finest scales and
here you can see a sketch of typical modeling at all institutions of you have a global model which you can see on the this for instance here and you see large-scale structures which are for instance Rossby waves which you can you can see here and they break and by doing this filaments in the vorticity field and then if you go and this is the end up in part of the troposphere if you go higher up for instance in the and measles here you can see these which we in which you can see it is as an to Newton clouds and these are immediate skip scale features and and then you have to assimilate holiday break and you end up divide holiday atmosphere dissipates the energy it depends on the smaller this effective processes which happened here on the grid scale of all Americans modern 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 2 intermediates gives you and then you have the dissipation scale here and clearly it is very difficult to have all these processes in 1 model and and 1 viewpoint and has a similar part of similar
problems are also not to be seen at other institutes not only did I appeal as these kind of modeling but also other institutes like uh the ideal reader of Irish stress Institute of the truck was instituted doing this kind of computational fluid dynamics and atmospheric all ocean it flows and all face this this whole range of orders of magnitude of magnitude so for instance the virus and have of the virus trans Institute is inserted and interested in how to model a geostrophic balance this is also very important for my own modeling and if you want to have to simulate that the who atmosphere you have to keep the geostrophic balance so this is the 1st dominate imbalance in the atmosphere you have to keep a try at then on this intermediate scale a lot of of of institutes are of faced this turbulence modeling business especially for instance also the triples and also did I will be in Institute of Boston for sure but also some aquaculture institute which CompuAdd heat fluxes and undermined by bonds but for instance Witcher is a small scale process but still very turbulent and a very important and then on this very small scale and then you have dissipation your time and dynamic the consistency is a very important topic because it's a it's hollow energy is actually dissipating so if you are consistent with the 2nd law of thermodynamics you know that all your energy is really dissipated and not of created out of nothing and then we have to institutions which are which are doing all kinds of orders of magnitude with often system but some Institute for clear clean foreign portion of which X 2 orders of spatial scales also very large temporal scale so and
and this is what we realized and all last and as many workshops and because these topics vessel because we had to 1st find a common language and we have to 1st be aware added everybody of us has a different history background and culture and if a mathematician talks about the way if it's not the same as in mutual just talks about a vapor and therefore we have to would be of very of all our diverse backgrounds but we have to acknowledge that this the diversification really takes place and therefore we have to somehow organize all know ledge and organize all methods and on nice also for that I think this is a very important topic for the future this was what discussed 1st
and then we define some gold for collaboration in this uh as many workshop and we thought about how to organize cocoa collaboration between the Institute which are dealing with competition fluid dynamics we thought that it would be good to have 1 institution as a junction point which would be good of Irish press Institute because so it keeps in touch with applied mathematics and it could can go into some depths that other institutions cannot go into a and we decided that it could be a good idea to have a court supervision of Bachelor of the rows seasons on Mars has seasons and otherwise could help and sharpening mathematical part of the proposals and help in solving mathematical problems and clearly we should continue with all the this summer schools of many workshops or whatever kinds of exchange platforms so and this is what
has been established since the last many workshops or which we could define existing or so ongoing collaboration between diverse institutions of term life units of the mine shaft so we have to have Irish Times Institute somehow in the center and the have other institutions and we could say that and there already common interests or a collaborations going on so for instance of was the Institute and know exactly how it was assigned to even when I have not yet partitioning the culture touching this form of bonding or they born in yeah so there's a collaboration between the triples and ATP about 2 relenting fluxes boundary conditions and this flows in animal advanced then there's a common interest between the virus was Institute and the truck was instituted modeling press on prismatic rates then between the Institute of Atmospheric Physics and the violations Institute is the thinking about structure preserving modeling and improving of accuracy of operators and then there's a long connection between the Institute of what's important and the Institute of Atmospheric Physics about turbulence modeling and this is because we are so close together as a wonderment is about 30 kilometres away from the ball and then we have are ongoing and collaborations for of this Institute for your this type system 1 of virus does Institute of so there is a girl with support for solutions of the technical problems from the virus stress Institute for either the because this it will fucose tied solution what Institute high-performance electronics and then there's also the collaboration between by National Institute and geophysical research the data deserve had for the 2 physicists in sharpening and mathematical aspects and research proposals so there's a lot of collaboration already ongoing this all of our network is not only on a sheet of paper really doing something and as for
proving fashion and is really the case I want to focus on some special topics which are known really here of a really interesting for several partners in safety and energy of the so for instance the topic of German common enemy consistent modeling and the shortly show an example an example and then reverse structure-preserving methods and that avoid on physically numerically used in the abilities and turbulence modeling which is a topic which every CFG G of 51 interest is interested in and most of these topics and I can all or most of the topics we are doing research and can take at least 1 of the 3 of them properties of a of a numerical scheme namely consistency accuracy and efficiency and some institutions want to be more efficient and I want to be more acute accurate and other institutes all whether it's consistent or not doesn't matter for the short time scales I'm interested in the consistency is not so important so these are the domain topics and here's an example for instance
of common interests between the more common interest of completely different from completely different backgrounds for instance at the last minute trough of often try presented an example in electrochemistry and this was of which to use this to the floor of an electorate and in a in a battery and hold the ions are moving forward and back and how they are diffuse and and there was a problem that some of thermodynamically consistency was not met in the altar of model which was set up by announced and planning and in this old model of did concentration of some items of plant so was bit besides that of an electric potentially only driver this flux and this inconsistency was or it was said that that's the internal consist inconsistency in power in the thermodynamics was caused by affected that the barycentric velocities man not could correctly computed and at the different pressure loss of the constituent in the electrode was not taken into account and and therefore the interaction between the different items that were not captured correctly and they're fun goes into the analysis of his more consistency and more stringent and thinking and comes up with a with a new flux formulation here which especially at pressure gradient him and 1 can see that the distribution of the different ions of this or on that that the distribution of ions here as a distance from 1 of 2 Underwood or cut to it I don't know but difference and all model from the New models and wired do I bring this example because the modulatory and in which logical modeling we
have a very very it's similar problem and favorite and it was can be traced back to a similar to a similar deficiency in the old viewpoint for instance we are usually we we are dealing with a mixture of criteria and water vapor from and so for instance for order of operations from the ground if you bring up a lot of vapor in the atmosphere and it it it will be diffused and in the conventional setting is stated as water vapor flux is just given by the gradient of the specific humidity it and then is in a similar way as the example was that and yields and patterns you have criteria and a lot of a product which is a mixture in the same way and all also all problem was that we had some include the inconsistency in the the duration of the creation and finally we got a new form of the formula all of which differs from the old form a lot especially by a term which is goes also with the gradient of the pressure of you and if you say that the level of the liquid of pluralism of more times t is probably proportional to the pressure so we have to do this pressure gradient was added in
the new few points for the electrochemistry example and in a similar vagueness was
added in there we deal with chicken example where you have dry air and water vapor and and also in this in all something you see that the alter a solution is a bit different from the new solution to new solution you have a bit more than hanged stopwatch water vapor flux so this
was 1 example that we can see that from totally different from the topics we have no common problems and now all the half 1 of these change the topic and become to the problem of the atmosphere and ocean modeling under 4 on the basis of the Navier-Stokes situation so we have a dry air and no water vapor and we have also been compressibility incompressibility and then I learnt from the Alexander that's it you should solve was for the Navier-Stokes equations the balance between the pressure gradient and between the false which could be here the cool URIs for us is not that we presented and that if 1 represents if 1 that takes an account that most of this forest is as it is balanced by gradient and then 1 can of 1 can
find that that but give geostrophic balance is dominating the who would momentum equation
of 2 Navier-Stokes equation and 2 of and that
large parts of the pressure gradient is
balanced by the Coriolis force but only large parts so the background so and now do you show up in or classical so levels of the Navier-Stokes equations and on not able to correctly simulate this geostrophic balance and therefore are letter lead to solutions which are completely unrealistic and shortly explain what this what this solutions are you all know that we have not large ocean basins for instance the Atlantic Atlantic Basin instead of going for a stroll that kind of current is going on there the western coast of this of this Atlantic Basin and the most simple mathematical model for this that's the data Gulfstream is only on the western side and is the so-called stomach drier which is this is a typical motion graphic problem and the court solution looks like this so you have the most locals on the western coast was there classical solution of the Navier-Stokes equations you would not see that most of this of this current is going on the West Coast and this and the background is that this the geostrophic balance is not correctly assimilated and if you would go into the details and for instance derived a discrete what city equation you would also the quickly see better problems is coming from and this is 1 example of everyone to launch
an minute equilibration and then we have a 2nd example which we are already working on and we had a meeting on this was that I had a problem which I could not so and I could ask some expert from the Weierstrass Institute to help me along with this and and the problem here is that I want to simulate a correct momentum diffusion tensor of which looks at as a fraction for the rest of the velocity and uh it's uses a frictional heating source this is a loss in the kinetic energy and the again in the internal energy and this structural of this this is a mathematical structure of product rule of differenciation should be preserve during the discretization and that of the of working on How to discretize these deformations e and f on hexagonal based regret and the
problem here is that the stumbling and is that on the deformed grids like to BC here to to be seen here our deformations which occur in this tends or are not accurate enough and our outcome of all 1st meeting in generative models that the improved accuracy of deformations by reconstruction directional gradients while a polynomial reconstruction as you can see here so and the background of the rules stuff is that on the on the sphere it is very and it is also importance to have a you have to have a good coverage of after the surface of the feel of the sphere was great book that points of grid boxes and there's still a hexagonal shaped good boxes of very fortunate end the and the have a model which works on on hexagons on this year and this is called the predictive Adam yeah and it OK that's not come
to the summary so we have implemented a minibatch of and see if and GFT in last September and we have also created some collaborations for instance as as a radius the show when we have now we want to develop a lot of pressure was scheme for the sphere of which means that we want to keep the geostrophic balance of well defined and this should also be a developed for compressible flows and the year of working together in improving the accuracy of the model momentum diffusion tensor and then we have this example with the heat fluxes and boundary conditions in animal bonds will most like Nord and somebody from the Agriculture Institute of working together of to solve the problem with the animal bombs and then we have all still part of a collaboration of which resulted in a draft proposal and simulations for geothermal energy and is submitted to the and and this was a collaboration between the act and lifeless Institute so we want now to continue the MMS phase and in the presence workshop the court tomorrow we will have many workshops also and see if energy of the and and I think the good idea to are of promote interdisciplinary exchange and collaboration within the light that's Institute thank you very much
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Numerische Strömungssimulation
Datenfeld
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Titel On perspectives for common research in the Leibniz MMS network in the field of Computational and Geophysical Fluid Dynamics
Serientitel The Leibniz "Mathematical Modeling and Simulation" (MMS) Days 2017
Autor Gassman, Almut
Mitwirkende Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
Institut für Atmosphärenphysik Kühlungsborn an der Universität Rostock (IAP)
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.
DOI 10.5446/21912
Herausgeber Technische Informationsbibliothek (TIB)
Erscheinungsjahr 2017
Sprache Englisch
Produktionsjahr 2017
Produktionsort Hannover

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Fachgebiet Informatik
Abstract Computational Fluid Dynamics (CFD) and Geophysical Fluid Dynamcis (GFD) are common research topics of different Leibniz institutes, where very similar mathematical and physical modelling approaches are used. Therefore, CFD & GFD seem to be obvious candidates for interdisciplinary research in the Leibniz Association. In the talk, an overview is given about the first common MMS research activities in the field of (CFD & GFD), and some perspectives for common research are presented.

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