Diagnostic wind models in urban air quality modeling

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Diagnostic wind models in urban air quality modeling
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CC Attribution 3.0 Germany:
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2019
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English

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Abstract
Diagnostic wind models (DWM) may present a feasible choice when full computational fluid dynamics (CFD) is not applicable due to unbearable numerical costs. For selected cases with DWM, it is possible to derive high resolution wind fields in a fraction of time needed to solve the Navier Stokes equations with a comparable quality. DWM solve an optimization problem under the constraint of mass conservation. The initial wind field is interpolated from measurements or a coarse-grid numerical weather prediction model application. Obstacles placed in the wind field are considered by a wake parameterization, which corrects the wind field for the momentum deficit by decreasing the wind speed or reversing the flow in the vicinity of obstacles (Roeckle, 1990, Nelson et al., 2008). The optimization problem is formulated in minimizing the deviation to the modified initial wind field. The solution is a vector potential of the desired wind field, which makes this approach inherently mass conserving. An important application of DWM is in urban air quality modeling, where street-canyon resolving wind fields are required for the realistic computation of emission dispersal.
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Partition (number theory) Population density Field (agriculture) Constraint (mathematics) Constraint (mathematics) Maxima and minima Equation Continuous function Mathematical optimization
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thank you and I am currently working with that the diagnostic when only which I use for 1 air quality moaning in night siege
and I want to show some basic concept this model so what's the idea behind
diagnostic wind motives we have given a wind field on a coarse grid and for example from USA skating well motivated and would like to protect this 1 of finding the resolution great which also contains the billing information so that we really can resolve this and street canyons and therefore
diagnostic win models solve only the continuity equation and no order dynamic equations so they
are quite simple and we also have the so Icarus efforts at deficit in comparison to forward to forward contemplation of fruit knowledge but nevertheless then and if the momentum seems op at arised accurately this users can also really percent an attractive choice as we can see if you can see you know and by this quick money ever
aeration this performs quite well in comparison to this dynamic for clearly this mode which I show is not as complex as this would list and yes so this is the
basic workflow flow of and and
such a model so the 1st step is we just blew by linear interpolation of their course when feed on the mesh with the desired resolution then we have given the
billing geometry that star and we create this they on a mesh and we it then must apply and this Waters's parameterization station to account for the momentum sinks behind the buildings and peel and it is sketched this and parameter session which was invented by the German engineering 1909 date so he 1st proposed this concept have given here the billing and then this wake cavity is itself a let ellipsoid shape and the length of this and is the to remind by The basic and billing geometry or by the dimension so what what what we then do is just to reverse the horizontal wind within this cavity and we also need
to parameterize the transition zone which use cord to
wake them from I I have done this with approximately and 75 thousand and then the wind field looks like this so it is not physicality at reason they will yet because we have just done some adjustment and and
there's still mean a there needs to be a mass consistent that's what's the that next step
is and what it's probably the most interesting part of 2 small leaves so with search for wind field
which is similar but to this initialized and which also solves the continuity equation as a constraint so we can formulate this correlational problem so we need to minimize their norm of the difference between this
wind fields and so this problem can then be and simplified if we
already have our solution which solves this equation and this can be any arbitrary solution so the most simplest ways just to integrate the worry color component and these density drone so there is no con- density change we can an approximate with their skating motor
and then if we just at this and solution and
subtract it then we we have this constraint so now we just search for field which and divergent free from this problem it is
quite easy to feels quite straightforward to derive you're like orange equations and this is
given here with the Lagrange multiplier and if we meet if you
apply the above chance we end up with this equation which we and need to solve a number so now the next an interesting question is
how do we make this discretization so this is a simple men thought this constant conservative and here I have and prodded the grid cell and they wind it is defined as the seller faces and the the Vergennes as warrior magic quantities defined in
the solution books and solar we though is to calculate this and flow balance in integral
form and this in stem then the divergent of this balance we can then and set up a matrix therefore and we need to look and we shape this three-dimensional vector field into our 1 dimensional vector field and then the next and stand just economy index of the matrix and if we do this similar uproar so then for the above chance then the in exams to rolling X of the matrix and this is that they that column the size and this is the number of moles so we have the linearized is a predator release quite to the simple but now and then the
idea is to introduce Billings into this this scripted session because we know that it's quite intuitive that Billings and are also close that and reviews they surfaced effective so of grid cell and
therefore I calculated for this meeting geometry late I can't
collated these flow permeability factors which leave which are defined also on the cell faces and here I've shown 2 fields in 2 different directions so fulfilling X director of a flow in y-direction and we you can see there is quite strong and use appropriate so for example here the flow is an opening next direct him up look in y-direction so we can already to
obtain an idea how this wind field and then looks like if you this mass consistent slides
bent so this this set of factors can use to spend a dime on on matrix and if we multiply this then to the the evidence matrix we Korek this session effective so face so if we put everything together and then we end up with this equation and critized the diet the gradient by taking the transpose of the divergent so this system is symmetric aside huge advantage mother it's really huge for the given problem so we have 5 millions of equations and we
need to solve this efficiently and therefore will
and IEEE applied to geometric Amodu that method which is quiet and pop allow for solving such problems I don't want to do and go the bind to this so the basic idea is that you discretized program on a serious off Of course great and
then and apply these tool great psyche by corrosively so you far yeah 5
smoothing out operation which which approximates and the solution on undefined rate then you calculate the residual Iuliu interpolated on the coarse grid and then in you and can and approximated low frequencies of Darrell which can then be interpolated direct 1 on the fine group to correct their assumed the solution so this and I will remove it gives an a fast common convergence which is and irrespective of 2 grid size as compared to you sure I'll iterate disorder so this is
so and a convergence test of different methods I was a tested the conjugate gradient method which and for this type of problem and fade because then the condition number of the
matrix A history I the to this permeability factors
but the more integrate math up to and already performed quite well they're using would do it as a precondition of for the Gate gradient method and only new obtains fast convergence and you just need a few iterations to make to obtain DeVore transferring the windshield so
this if an example of
of a song if the missiles on the Giants of this mass consistent wind faint which we obtained so this shows the station building and as you can see now it really the flow adapt to these and to this channeling effects and also in the world to verticality no mention you can see how this and Waters's develop as a consequence of these so that imitation and what this
optimization problem here in this
the stream this streamlines inside this stadium also there are I walked IX the developed you can see
also this walked assists in Viterbo 2 by the distribution of the book Codd and also the so we have lots of up-and-down wins where we have Millings present and this take in extends or up who opt to their highest layer of the the main you can even seen 200 meters and of course and structure of the city
I use this the Winfield to and to just perform a very simple effects and I am therefore use that and both emissions they emissions so along their most important quotes now
you can really see how the billings then their dispersion
of this and tracer so here you can see and because you have up mixing their mind on mixing of keen L so that the flow is from the southwest and you can really see these chilling Effects nicely also there are is submitting present and you can see that You're Barry's keener us informed of 2 billing and 70 meter
I Institute you you can see where this is mixed out from the street level and that's basically where you have the largest Millings present because then you also have the largest poultices which makes this app efficiently so this
what's this idea of this model which I wanted to present and
I thank you for your attention at the
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