Scientific and High Performance Computing
Peter Deuflhard (BISEC, China)
Rupert Klein (FU Berlin, Germany)
YvonMaday (Université Pierre et Marie Curie, France)
Gabriel Wittum (KAUST, Saudi Arabia)
Pingwen Zhang (Peking University, China)
Traffic Modeling and Simulation
Yanyan Chen (BJUT, China)
Rolf Moehring (BISEC, China)
Zijun Wu(Hefei University, China)
Kai Nagel (TU Berlin, Germany)
Heng Wei (University Cincinnati, USA)
Joe Zietsman (Texas A&M Transportation Institute, USA)
Environmental Modeling and Simulations
Eva Gutheil (IWR Heidelberg, Germany)
Siegfried Raasch (Leibniz Universität Hannover, Germany)
Pierre Sagaut (Aix-Marseille University, France)
Hans-Stefan Bauer (University of Hohenheim, Stuttgart, Germany)
City Reconstruction, Mesh Generation and Data Visualization
Hans-Christian Hege (ZIB, Berlin, Germany)
Leif Kobbelt (RWTH Aachen, Germany)
Klaus Mueller (Stony Brook University, USA)
HuaminQu (Hong Kong Univ. of Science & Technology, China)
Sebastian Reiter (University Frankfurt, Germany)
Han-Wei Shen (Ohio State University, USA)
Hang Si (WIAS, Berlin, Germany)
Xiaoru Yuan (Peking University, China)
Pollution and its Impact on Humans
Jingnan Hu (Chinese Research Academy Environmental Sciences, China)
Karin Moelling (University of Zürich, Switzerland)
Mike Roberts (University of Queensland, Brisbane, Australia)
Title：Parallel Adaptive Computation of Environmental Flows
Organization：KAUST, Saudi Arabia
Numerical simulation has become one of the major topics in Computational Science. To promote modeling and simulation of complex problems new strategies are needed allowing for the solution of large, complex model systems. Crucial issues for such strategies are reliability, efficiency, robustness, usability, and versatility.
After discussing the needs of large-scale simulation we point out basic simulation strategies such as adaptivity, parallelism and multigrid solvers. To allow adaptive, parallel computations the load balancing problem for dynamically changing grids has to be solved efficiently by fast heuristics. These strategies are combined in the simulation system UG4 (“Unstructured Grids”) being presented in the following.
In the second part of the seminar we show the performance and efficiency of this strategy in various environmental applications. In particular, the application and benefit of parallel adaptive multigrid methods to modelling environmental flows.
Title：Predictor Reconstitution from Data
Organization：Peking University, China
Predictor reconstitution method is a modeling based on the data concluded from the weather consultation of the forecasters. By means of machine learning, this method can reconstitute the predictors of European Centre for Medium-Range Weather Forecasts (ECMWF) model combined with the observations and give the weather forecast results. As an example, we used this method to forecast the temperature at the Yanqing weather station of Beijing (a station nearby the Yanqing Zone of 2022 Beijing Olympic Winter Games) and that in the whole Beijing area respectively. Compared with classical Model Output Statistic(MOS) prediction, predictor reconstitution method can dramatically improve the accuracy of temperature forecast and reduce the root-mean-square errors.
Title：The Parameterized-Background Data-Weak (PBDW) formulation for data assimilation: application to outdoor air quality models and noisy data
Organization：Université Pierre et Marie Curie, France
Reduced basis methods allow to perform efficient numerical simulation of complex implicit models depending on parameters. In the same lines, these model reduction techniques have been extended to explicit reconstruction of functions. The Parameterized-Background Data-Weak (PBDW) method allows data reconstruction combining an underlying parameter dependent model with data fitting, these data possibly being polluted with noise. The PBDW approach extends the (Generalized) Empirical Interpolation Method, and allows to correct the bias inherent to simplified models. The effect of noisy data can be minimized by taking into account in a proper way the notion of Kolmogorov n-width. In this presentation we shall explain in detail the basics of the nonintrusive PBDW approach and the way the notion of small Kolmogorov n-width can be used in practice to provide rapid and efficient data assimilation approaches. The application to air quality case studies will also be presented with a particular attention on the care of physical dimension of the phenomenon under investigation.
Title：The Role of Traffic Optimization in BISEC’s Environmental Project
Speaker：Rolf Moehring/Zijun Wu
Organization：BISEC, China/Hefei University, China
Emissions from car traffic contribute a significant part to the overall pollution of a city. We will outline an approach how these emissions can be integrated into the computational modeling of air pollution with atmospheric flow models that are the core of BISEC’s Environmental Project. This integration is the basis for investigating to which degree different traffic patterns will change the overall pollution. Such traffic patterns can be obtained by traffic optimization methods such as congestion pricing or route guidance and we will outline some of them.
Title：Microscopic simulation of taxicabs and autonomous vehicles with MATSim
Organization：TU Berlin, Germany
From a transportation planning perspective, autonomous vehicles (AVs) can be seen as a mode of transport: Rather than, say, walking to the car and then driving, or walking to the pt stop, waiting, and then boarding, one would request an AV, wait for it, then board, etc. This can be simulated microscopically, where microscopic means that there are as many synthetic avatars as there are persons and vehicles in reality. One interesting problem is real-time dispatch. I will show results from simulations that reach up to synthetically replacing one million privately owned cars in Berlin by a fleet of 100'000 AVs, and then derive some policy recommendations based on these simulations. These include results for making that fleet electric, and thus (locally) free of emissions.
Title：Noise Barrier Based Measures for Reducing Traffic Pollutant Impact on Communities near Freeways
Organization：University Cincinnati, USA
Numerous health studies conducted worldwide suggest an increase in the occurrence of adverse health effects for populations living, working, or going to school near large roadways. Extensive studies have been carried out focusing on reducing the traffic-source noise and vehicle emission induced pollutants via various structural means such as noise wall or other barriers near major highway infrastructures. Noise barriers can reduce noise levels from traffic by blocking and deflecting sound waves. Meanwhile, noise barriers adjacent to a roadway may also inhibit lateral air movements off the road, leading to elevated on-road pollutant concentrations. This presentation will present typical approaches for examining effect of roadside features on near-road air pollutant exposures and evaluation of near-road air quality without barriers and with a noise barrier, as well as design principles for the community. Finally, a synthesis of reducing the impact of traffic-source noise and air pollutants on nearby communities through equipping the nanostructured faraday energy converter within the noise wall will be introduced.
Title：High Resolution Modelling of Urban Canopy Layer Processes For Large City Areas
Organization：Leibniz Universitaet Hannover, Germany
Originally applied to study convective atmospheric boundary layers (CBL), large-eddy simulation (LES) is meanwhile used in many fields of science. This is mainly the consequence of a massive increase in available computer resources. State-of-the-art massively parallel computers have opened the field for a wide variety of new applications. On these machines, simulations with extremely large numerical grids of up to 40003 grid points and even more are currently carried out in acceptable time. In Meteorology, beside fundamental research LES starts to be used also for more applied topics like air pollution modeling, flow around buildings, or wind energy. Computational resources nowadays allow to simulate complete city areas with very high spatial resolution down to the meter scale. Precise simulations on this small spatial scale require explicit representation of various physical aspects like the energy balance of building surfaces, the effects of plants and trees, or radiation modeling that includes reflection from building walls. Furthermore, recently developed models also include gas phase and particle phase chemistry to study air quality problems. The talk will start with a short general introduction to LES and will then give an overview of current studies at IMUK concerning simulations of the urban canopy layer. Beside results from these studies, a focus will be given on the technical features of the PArallelized LES Model (PALM), that has been developed at IMUK during the last 20 years, including parallelization and optimization. Within the German wide project [UC]² (Urban Climate Under Change), PALM is currently significantly extended to include various processes mentioned above, that are relevant for urban canopy studies. The extended model PALM-4U (read PALM for urban applications, or PALM for you) will be explained and first simulation results will be presented. The problem of providing initial and boundary conditions for large areas on small spatial scales will also be addressed.
Title：Modeling and simulation of particle-laden reacting flows and their impact on the environment
Organization：IWR Heidelberg, Germany
The presentation concerns the modeling and simulation of the interaction of particles in turbulent reacting flows with special application to environmental issues including traffic pollutants and ozone depletion in the tropospheric Arctic spring. The governing equations for the particle-laden turbulent reacting flows are presented and discussed with focus on the interaction of turbulent mixing, evaporation and chemical reactions, which strongly interact in these systems. In particular, transported joint pdf (probability density function) methods are addressed and (spray) flamelet models are analyzed and discussed for the consideration of detailed chemical reactions that allow for the prediction of combustion-generated pollutants. These may affect the global environment in terms of ozone depletion in the tropospheric Arctic spring. The numerical solution schemes require the consideration of the particle phase in terms of source terms representing the dilute particle phase.
Title：Lattice-Boltzmann simulations for pollutant transport and Urban Physics in full-scale realistic configurations
Organization：Aix-Marseille University, France
Lattice-Boltzmann methods have been proved to be a very efficient approach for computational fluid dynamics, including applications related to civil engineering and urban physics. The talk will illustrate recent results in the field obtained using the ProLB solver, co-developed by Airbus, Renault, CS-CI, EcoleCentrale de Lyon and Aix-Marseille Université. Typical applications are related to large-eddy simulation of pollutant transport and wind engineering problems in full scale configurations (up to 2-4 km2 of realistic urban areas with a mesh resolution about 0(10 cm)). The physical model includes a full micrometeorological model, turbulence modelling but also dedicated submodes such as vegetalized areas and volumes. Coupling with uncertainty quantification methods to account for randomness in wind conditions a pollutant source definition will also be discussed, along with reconstruction of pollutant source location and incoming wind conditions via Data Assimilation.
Title：Investigation and Evaluation of Atmospheric Processes in Orographic Terrain Applying the WRF Model with Very High Resolution: Examples from Selected Cases
Organization：University of Hohenheim, Stuttgart, Germany
Numerical models have long been used as tools to better understand atmospheric processes and their evolution. In recent years, simulations with finer and finer resolution have been applied for this purpose.
To serve process understanding and model evaluation, we apply the WRF model in a chain of simulations from the mesoscale down to a resolution of 100 m. In the fine scale domain, WRF is applied in Large-Eddy simulation (LES) mode with switched-off turbulence scheme, permitting to simulate most of the energy transporting eddies explicitly. Advantage of WRF, as compared to “traditional” LES models, are the possibility to set up the system for real atmospheric cases, namely with realistic lower boundaries and meteorological forcing from the ECMWF operational analysis. Furthermore, a consistent set of physical parameterizations is applied through the whole chain of simulations.
The evolution of the convective boundary layer on a sunny spring day and the life cycle of a supercell that developed over southwestern Germany on 30 June 2012 are selected as examples to present the capabilities of the system.
The results are very promising and demonstrate that WRF can be applied at such high resolutions for detailed process studies.
Title：Visualization of Environmental Information – A Survey
Organization：ZIB, Berlin, Germany
This talk surveys the state of the art of visualization of environmental information, focusing on techniques for visually supported analysis of meteorological data, pollution transport and traffic-related information. After addressing data related aspects, like data acquisition, data fusion and data management, the characteristics of the various data and the related analysis tasks will be examined. Some visualization solutions will be exemplarily presented. From the many aspects to be considered when developing a comprehensive visualization tool, the specific aspects of scalability, uncertainty visualization and decision support will be discussed. The talk ends with a presentation of current challenges and future research tasks.
Title：Meshing and distribution of unstructured, adaptive grid hierarchies for large scale parallel multigrid simulations
Organization：University Frankfurt, Germany
The generation of detailed three dimensional meshes for the simulation of complex physical processes is crucial to capture important properties of the underlying domains and to reach a satisfying accuracy. At the same time this level of detail poses high demands both on suitable hardware and numerical solver efficiency. Parallel multigrid methods have been shown to exhibit near optimal weak scalability for massively parallel computations in various applications. A crucial step in using parallel multigrid methods is the creation of detailed distributed meshes and underlying grid hierarchies. In our simulation software UG4, we employ a highly scalable interweaved refinement and redistribution approach to parallel mesh generation which supports anisotropic and adaptive refinement schemes on unstructured, hybrid grids. We present the meshing software ProMesh, which provides a rich variety of tools to ease the process of coarse grid generation for the described parallel mesh adaption approach. Applications from different research areas are presented to underline the efficiency and applicability of the described approach to massively parallel computations.
Title：Challenges in 3D Unstructured Mesh Generation and Adaptation
Organization：WIAS, Berlin, Germany
In this talk, I'll first give an overview of state-of-the-art of 3d unstructured mesh generation, including
- boundary constrained mesh generation,
- adaptive mesh refinement,
- mesh quality improvement, and
- anisotropic mesh generation
I will then discuss some challenging problems in tetrahedral mesh generation and present some recent research results on these problems.
I will finish with some expectation for developing a parallel tetrahedral mesh generator.
Title：Large Scale Distribution-based Data Analysis and Visualization
Organization：Ohio State University, USA
Scientists overview and identify regions of interest by transforming data into compact information descriptors that characterize simulation results and allow detailed analysis on demand. Among many existing feature descriptors, statistical information derived from data samples is a promising approach to taming the big data avalanche because data distributions computed from a population can compactly describe the presence and characteristics of salient data features with minimal data movement. The ability to computationally summarize and process data using distributions also provides an efficient and representative capture of information that can adjust to size and resource constraints, with the added benefit that uncertainty associated with the results can be quantified and communicated. In this talk, I will discuss our recent works on using distributions as a new paradiagm for representing large scale scientific data sets. Our goals are to ensure that scientists can easily obtain an overview of the entire data set regardless of the size of the simulation output; understand the characteristics and locations of features; easily interact with the data and select regions and features of interest; and perform all the analysis tasks with a small memory footprint.
Title：Generation of 3D Models for Simulation with Particular Applications in 3D City Reconstruction
Organization：RWTH Aachen, Germany
The generation and optimization of digital 3D models is a crucial but also difficult step in most simulation workflows. The difficulty arises from a number of special quality requirements that the 3D models have to satisfy in order to guarantee efficient and reliable computations. While overall, simulation workflows recently exhibit a high degree of automation, the pre-processing of the geometric data (i.e. „meshing“) is still a mostly manual and hence costly process. In this talk, I will present some current trends and advances in automatic mesh generation and optimization that effectively reduce the amount of user intervention while still enabling full control over the result.
As one particular example, I will address the generation of 3D city models. Here, the acquisition of raw data is challenging because it often has to be combined from different sources. Furthermore, there is a wide range of detail levels to which individual building need to be adjusted to provide enough detail (only) where it is required while still keeping the overall complexity of the city model (potentially with thousands of buildings) within reasonable bounds. I will present a framework which generates the vast majority of buildings procedurally, yielding plausible visualizations for structurally simple (residential) buildings. For structurally complex landmark buildings a procedural approach does not achieve satisfactory visual fidelity. Thus, we employ image-based techniques to reconstruct them at a higher degree of realism. As the manual acquisition of data required for the procedural and image-based reconstructions is practically infeasible for whole cities, we rely where possible on publicly available data as well as crowd sourcing projects. This enables our framework to render views from cities without any dedicated data acquisition as long as there are sufficient public data sources available. To obtain a more lively impression of a city, we also visualize dynamic features like weather conditions and traffic based on publicly available real-time data.
Title：Visualizing Human Activities in Big Cities
Organization：Peking University, China
Understanding the complex nature of activities in modern metropolitan regions are difficult due to the vast amount of data required for processing and analysis. Visualization provides essential accesses for users to comprehend such big data and gain insights, which is crucial for decision makers, political figures, as well as the general public. This talk will discuss visualization cases covering various types of urban data, including vehicle GPS and RFID records, subway IC card logs, mobile phone signals, social media data and simulation data. We will demonstrate how different data sets can be integrated for advanced visual analysis. With the assistant of properly designed visualization and interaction, both general public and experts can interactively conduct the data exploration, mental image construction, and insight discovery.
Title：Viruses all over
Organization：University of Zürich, Switzerland
Viruses are the most successful biologiclal species on our planet. They may have been first, 3.8 billion years old - and may be the last ones surving us all.
The viruses are known today as pathogens, as parasites of cells, unable to replicate independently. Yet they are the most successful species reaching 1033 - more than stars in the universe.
They are present in our environment, in the oceans, the soil, the air, and inside and outside of all living species including men. What was their role at the beginning of life? And later? What are they doing today?
Most of them are known as causes of disease, such as Influenza, Hepatitis, HIV, SARS. Also bacteria are considered as mainly dangerous pathogens. But those are in numbers in the vast minority. Their overestimate is based on medical history. In constrast, recently new technologies such as gene sequencing indicate that most of them are present with important functions for the benefit for life on earth not death. They are presently characterized in toto as microbiome or virome, which comprises all bacteria and all viruses together without individual knowledge. They are involved in recycling of food chains in the oceans, populate all species, inside and outside, contribute to digestion of food, protect us against foreign microbes, they are the drivers of evolution and they have played a major role in building all genomes including humans, by mechanisms such as horizontal gene transfer. There they make up almost 50% of the sequences. We are viral!
The world of viruses has recently been extended by the discovery of giant viruses which were even detected in permafrost and are hosted by amoebae. They can be bigger than bacteria and can be condsidered as the missing link between the prebiotic world and larger living cells. their contribution to the orign of life is debated. It has become a focus of interest recently due to the discovery of exoplanets and the possiblity of habitable worlds outside the earth. Viruses transported by dust or smog are yet unexplored and worth analyzing.
Title：Toxicokinetics associated with air pollution and traffic in Beijing
Speaker：Michael S Roberts
Organization：University of Queensland, Brisbane, Australia
A key challenge in the computational modeling of Beijing’s air pollution and traffic to relate human toxicity with the extent of exposure of the various pollutants. In this paper, we have sought to characterise the toxicokinetics associated with Beijing’s pollution. We obtained estimates of the nature and concentrations for chemicals, (e.g. NO, NO2 and polyaromatic hydrocarbons) and airborne particulate matter (including their particle distributions) from the literature. We also searched for any reported data for these air pollutants based on internal and external exposure, physiological/biochemical/pathological effects and health service usage, including potential seasonal effects. We then applied various modelling techniques to interpret this data with a goal of providing predictions that may assist in reducing future toxicity arising from future air pollution in Beijing.
Title：Emission Inventory and Control Strategy of Mobile Sources in Beijing-Tianjin-Hebei Area
Organization：Chinese Research Academy Environmental Sciences, China
Mobile sources are one of most important air pollution sources in many regions or cities in China, especially in the Beijing-Tianjin-Hebei area, and adversely increase public health and climate burdens. To improve ambient air quality and mitigate emissions from mobile sources, high-precision emission inventory should be established to further develop and evaluate control strategies. This study collected large samples of real-world emission data and vehicle usage profiles in Beijing-Tianjin-Hebei area to develop the emission inventory of major air pollutants (e.g., NOX, PM, THC) for mobile sources. The results indicate that the mobile source emissions in Beijing-Tianjin-Hebei Area were estimated to be 0.97 Mt of NOX, 0.15 Mt of PM and 0.59 Mt of THC. Automobiles are one of the largest contributors to NOX, PM and THC, sharing 60.6%, 34.5% and 72.8% of total mobile source emissions, respectively. Scenario analysis suggests that an approach with no additional policy would not lead to the emission reductions that are required. Under the most aggressive scenario with tightened standards for emissions and fuel quality, restricted vehicle population, lowered vehicle-use intensity and large scale penetration of electric vehicles, the total vehicle emissions of NOX, PM and THC in Beijing-Tianjin-Hebei area in 2030 could be reduced by approximately 48%, 36% and 45%, respectively. On the basis of above analysis, the medium to long-term control strategy of mobile source emissions are proposed, for example, optimizing regional traffic structure and layout, implementing the unified standards of emissions and fuel quality, and constructing the fully green transportation. Therefore, this study can provide policy makers with useful first-hand information and significant support for better control strategies in mobile source emissions in Beijing-Tianjin-Hebei area.
Title：Modeling the Impacts of Traffic Emissions Reduction Strategies
Organization：Texas A&M Transportation Institute, USA
Traffic emissions are a major contributor to poor air quality, especially in urban areas. Strategies to reduce emissions from traffic can be broadly classified as improvements to vehicle and fuel technologies, transportation demand management, and transportation system management. Appropriate analytical tools and models are required to assess the benefits of implementing these different strategies. This presentation demonstrates the results of modeling transportation infrastructure improvement strategies (i.e. transportation system management strategies) at the regional/network level as well as the project level. The study was done using modeling test beds set up in the cities of El Paso and Houston, Texas. A multi-resolution modeling approach was used for the traffic modeling, followed by the application of the MOVES model to estimate emissions. Life cycle emissions impact (i.e. emissions from the construction and maintenance of the infrastructure) was also considered in the analysis. The findings demonstrate the importance of integrated modeling of strategies at the network level to identify effective strategies and optimize their implementation.
Title：Beijing traffic emission analysis and simulation based on big data
Organization：Beijing University of Technology (BJUT), China
Using Beijing as an example, this report introduces the background of Beijing's traffic development and motor vehicle emissions. Based on traffic and environmental big data, a dynamic simulation model of traffic emissions from the whole road network was developed, and thereal-time estimation and spatial-temporal characteristics of road emissions from motor vehicles were initially achieved. Then, we select policies such as congestion pricing in low-emission areas, and use big data and simulation models toevaluatethe effects.
Title：Visual Analytics of Human Mobility Behaviors
Organization：Hong Kong Univ. of Science & Technology, China
With increasing availability of location-acquisition technologies, including GPS devices on vehicles and in mobile phones, huge volumes of data tracking human mobility have been collected, which provides an unprecedented opportunity to study human mobility patterns. In this talk I will introduce three novel visual analytics systems developed at Hong Kong University of Science and Technology for analyzing human mobility patterns based on transportation and mobile phone data: 1) TelcoVis, a visual analytics system for the exploration of co-occurrence in human mobility of Guangzhou based on telco data. 2) SmartAdP: a visual analytics system for selecting billboard locations based on large-scale taxi trajectories. 3) PTSVis, a System to help transportation researchers visualize and explore passenger mobility in a public transportation system (PTS) based on massive passenger RFID card data.
Title：An Interactive Visual Analytics Framework for Multi-Field Climate and Pollution Data in a Geo-Spatial Context
Organization：Stony Brook University, USA
Climate and pollution research produces a wealth of multivariate data. These data often have a geospatial reference and so it is of interest to show them within their geospatial context. One can consider this configuration as a multi-field visualization problem, where the geo-space provides the expanse of the field.. In this talk I will present the results of several research projects I have been involved with in recent years: (1) a dual-domain interface that links a geospatial data display, such as an enhanced Google Earth, with a multivariate information display, and (2) a framework that can colorize geo-spatial maps and images based on multivariate data. Time permitting, I will also sketch a computational framework that uses the Lattice-Boltzmann Method for simulating gaseous phenomena, such as pollution in large urban environments.
Title：Atmospheric flow regimes, seamless numerics, and balanced data assimilation
Organization：Freie Universität Berlin, Mathematik & Informatik
The wide hierarchy of atmospheric scales and processes can be characterized utilizing concepts of asymptotic analysis. By revealing an intrinsic structural consistency amongst the many reduced dynamical models for specific phenomena known from theoretical meteorology, such a characterization lies the foundation for systematic studies of scale interactions.
Most of the mentioned reduced models are, on the one hand, relevant in that the related flow regimes are observed in nature. As a consequence, numerical simulation codes based on the full compressible aerothermodynamics of air should be able to reliably represent the associated flow regimes. Since, on the other hand, most of these regimes correspond to singular asymptotic limits, very careful design of "well balanced" numerical flow solvers is needed.
Because the instantaneous state of the atmosphere cannot be measured, its time evolution is not described in practice as an initial-boundary value problem, but rather in the form of a coupled forward modelling--data assimilation process. This process, too, is to adhere to the requirement of (partial) balance of flow states discussed above.
In this presentation, I will summarize each of these three problem areas and discuss recent contributions that have their roots in the ideas of multiscaleasymptotics.
Title：Computational modelling of heterogeneous smog reactions by adaptive discrete Galerkin methods
Smog reactions can be described by a huge number of ordinary differential equations (ODEs), typically a set of thousands up to millions of ODEs. Mathematically speaking, they can be conveniently formulated in the framework of countable ODEs (CODEs). In order to treat such CODEs, the author and M. Wulkow (1989) designed the construction of so-called discrete Galerkin methods, which lead to a small number of ODEs for basis elements in non-trivial sequence spaces generated from statistical kernels. For homogeneous chemical polyreactions, such methods have led to computational speed-ups of more than 10.000 compared to traditional methods. For smog reactions, heterogeneous polyreactions arise due to the fact that the chemistry takes place on the surfaces of smog particles. In contrast to classical finite element or finite volume methods, where right hand sides in terms of continuous quadratures arise, the right hand sides of the CODEs contain infinite sums, which can be efficiently approximated by either discrete multigrid quadrature or discrete Gauss-Christoffel quadrature. In the intended project on the Beijing environment the presented discrete Galerkin methods may be used either within spectral methods or as add-on in terms of low order smog models.