Air pollution modelling using a graphics processing unit with CUDA

The Graphics Processing Unit (GPU) is a powerful tool for parallel computing. In the past years the performance and capabilities of GPUs have increased, and the Compute Unified Device Architecture (CUDA) - a parallel computing architecture - has been developed by NVIDIA to utilize this performance in general purpose computations. Here we show for the first time a possible application of GPU for environmental studies serving as a basement for decision making strategies. A stochastic Lagrangian particle model has been developed on CUDA to estimate the transport and the transformation of the radionuclides from a single point source during an accidental release. Our results show that parallel implementation achieves typical acceleration values in the order of 80-120 times compared to CPU using a single-threaded implementation on a 2.33 GHz desktop computer. Only very small differences have been found between the results obtained from GPU and CPU simulations, which are comparable with the effect of stochastic transport phenomena in atmosphere. The relatively high speedup with no additional costs to maintain this parallel architecture could result in a wide usage of GPU for diversified environmental applications in the near future.Comment: 5 figure

Monte Carlo Algorithms for Linear Problems

MSC Subject Classification: 65C05, 65U05.Monte Carlo methods are a powerful tool in many fields of mathematics, physics and engineering. It is known, that these methods give statistical estimates for the functional of the solution by performing random sampling of a certain chance variable whose mathematical expectation is the desired functional. Monte Carlo methods are methods for solving problems using random variables. In the book [16] edited by Yu. A. Shreider one can find the following definition of the Monte Carlo method

Semi-Lagrangian methods in air pollution models

Various semi-Lagrangian methods are tested with respect to advection in air pollution modeling. The aim is to find a method fulfilling as many of the desirable properties by Rasch andWilliamson (1990) and Machenhauer et al. (2008) as possible. The focus in this study is on accuracy and local mass conservation. <br><br> The methods tested are, first, classical semi-Lagrangian cubic interpolation, see e.g. Durran (1999), second, semi-Lagrangian cubic cascade interpolation, by Nair et al. (2002), third, semi-Lagrangian cubic interpolation with the modified interpolation weights, Locally Mass Conserving Semi-Lagrangian (LMCSL), by Kaas (2008), and last, semi-Lagrangian cubic interpolation with a locally mass conserving monotonic filter by Kaas and Nielsen (2010). <br><br> Semi-Lagrangian (SL) interpolation is a classical method for atmospheric modeling, cascade interpolation is more efficient computationally, modified interpolation weights assure mass conservation and the locally mass conserving monotonic filter imposes monotonicity. <br><br> All schemes are tested with advection alone or with advection and chemistry together under both typical rural and urban conditions using different temporal and spatial resolution. The methods are compared with a current state-of-the-art scheme, Accurate Space Derivatives (ASD), see Frohn et al. (2002), presently used at the National Environmental Research Institute (NERI) in Denmark. To enable a consistent comparison only non-divergent flow configurations are tested. <br><br> The test cases are based either on the traditional slotted cylinder or the rotating cone, where the schemes' ability to model both steep gradients and slopes are challenged. <br><br> The tests showed that the locally mass conserving monotonic filter improved the results significantly for some of the test cases, however, not for all. It was found that the semi-Lagrangian schemes, in almost every case, were not able to outperform the current ASD scheme used in DEHM with respect to accuracy

PARALLEL COMPUTATIONS WITH LARGE-SCALE AIR\ud POLLUTION MODELS

Large-scale mathematical models are very powerful tools in the efforts to provide more\ud information and more detailed information about the pollution levels, especially about pollution\ud levels which exceed certain critical values.. However, the model used must satisfy at\ud least two conditions: (i) it must be verified that the model results are reliable and (ii) it\ud should be possible to carry out different study by using the model. It is clear that comprehensive\ud studies about relationships between different input parameters and the model results\ud can only be carried out (a) if the numerical methods used in the model are sufficiently\ud fast and (b) if the code runs efficiently on the available high-speed computers.\ud Some results obtained recently by a new unified version of the Danish Eulerian Model will\ud be presented in this paper

Assimilation of OMI NO₂ retrievals into the limited-area chemistry-transport model DEHM (V2009.0) with a 3-D OI algorithm

Data assimilation is the process of combining real-world observations with a modelled geophysical field. The increasing abundance of satellite retrievals of atmospheric trace gases makes chemical data assimilation an increasingly viable method for deriving more accurate analysed fields and initial conditions for air quality forecasts. We implemented a three-dimensional optimal interpolation (OI) scheme to assimilate retrievals of NO2 tropospheric columns from the Ozone Monitoring Instrument into the Danish Eulerian Hemispheric Model (DEHM, version V2009.0), a three-dimensional, regional-scale, offline chemistry-transport model. The background error covariance matrix, B, was estimated based on differences in the NO2 concentration field between paired simulations using different meteorological inputs. Background error correlations were modelled as non-separable, horizontally homogeneous and isotropic. Parameters were estimated for each month and for each hour to allow for seasonal and diurnal patterns in NO2 concentrations. Three experiments were run to compare the effects of observation thinning and the choice of observation errors. Model performance was assessed by comparing the analysed fields to an independent set of observations: ground-based measurements from European air-quality monitoring stations. The analysed NO2 and O3 concentrations were more accurate than those from a reference simulation without assimilation, with increased temporal correlation for both species. Thinning of satellite data and the use of constant observation errors yielded a better balance between the observed increments and the prescribed error covariances, with no appreciable degradation in the surface concentrations due to the observation thinning. Forecasts were also considered and these showed rather limited influence from the initial conditions once the effects of the diurnal cycle are accounted for. The simple OI scheme was effective and computationally feasible in this context, where only a single species was assimilated, adjusting the three-dimensional field for this compound. Limitations of the assimilation scheme are discussed

A new model of a tidally disrupted star

A new semi-analytical model of a star evolving in a tidal field is proposed. The model is a generalization of the so-called 'affine' stellar model. In our model the star is composed of elliptical shells with different parameters and different orientations, depending on time and on the radial Lagrangian coordinate of the shell. The evolution equations of this model are derived from the virial relations under certain assumptions, and the integrals of motion are identified. It is shown that the evolution equations can be deduced from a variational principle. The evolution equations are solved numerically and compared quantitatively with the results of 3D numerical computations of the tidal interaction of a star with a supermassive black hole. The comparison shows very good agreement between the main ``integral'' characteristics describing the tidal interaction event in our model and in the 3D computations. Our model is effectively a one-dimensional Lagrangian model from the point of view of numerical computations, and therefore it can be evolved numerically $10^{2}-10^{3}$ times faster than the 3D approach allows. This makes our model well suited for intensive calculations covering the whole parameter space of the problem.Comment: This version is accepted for publication in ApJ. Stylistic and grammatical changes, new Appendix adde

Numerical investigation of granular flow and dynamic pressure in silos

Although the flow of granular material in silos and the pressure acting on the silo walls have been studied for over a century, many challenges still remain in silo design. In particular, during the discharge process some dynamic phenomena in silos can often be observed to display large, self-induced and dynamic pulsations which may endanger the stability of the silo structure. The aim of this thesis is to study the flow and pressure in silos using numerical modelling and analytical methods, and to further understand the mechanical behaviour of granular material and mechanism of dynamic phenomena during silo discharge. The Finite Element (FE) method can be used to analyse the behaviour of the granular material in silos by considering the material as a continuum. In this thesis, FEM modelling of silo flow was developed using the Arbitrary Lagrangian-Eulerian (ALE) formulation in the Abaqus/Explicit program and the key parameters that affect the predictions of the flow and pressure during discharge were identified. Using the ALE technique, almost the entire silo discharge process can be simulated without mesh distortion problems. The mass flow rate and temporally averaged discharge pressure predicted by the FE model were first investigated in a conical hopper and were found to be in good agreement with those from the most commonly quoted theoretical solutions. The transient dynamic pressure fluctuations during incipient silo discharge were predicted and the causes for these dynamic events have been investigated which led to the conclusion that the stress wave propagation and the moving shear zone phenomena within the bulk solid were responsible for the dominant higher and lower frequencies effects respectively. A one-dimensional dynamic model of granular columns subject to Coulomb wall friction was developed to investigate the propagation of stress waves, focusing on the effect of geometry by examining converging and diverging tapered columns. The analytical solutions of this model are compared to the FE model based on the ALE formulation. This FE model was first validated using the known behaviour for cylindrical columns. In all cases, the stress impulse set off by incipient discharge at the silo outlet grew with the distance travelled up the column, however the rate was shown to depend on the halfangle of the taper. Over a range of small angles, the proposed analytical model was found to accurately predict this behaviour. After the successful application of the ALE technique for a conical hopper, the FE model was extended to simulate the granular flow in a flat-bottomed model silo. The FE predictions were compared with the silo pressure measurements in a model silo (Rotter et al, 2004). Pressure cells mounted along a vertical line on the silo walls were used to measure the pressure distribution in the silo tests using dry sand. The FE model was further extended to simulate the granular flow in a model silo consisting of a cylindrical section with a conical hopper. The prediction was compared with the experimental observations from a model silo (Munch-Andersen et al, 1992), together with the well-known theoretical solutions. Two numerical issues were addressed in some detail: one is the numerical treatment of the abrupt transition between the cylinder section and the conical hopper, the other is the interaction between the granular solid and the silo walls that was modelled using a dynamic friction model. In addition, the dynamic pressure events during discharge were examined and plausible explanations were given. Finally, this thesis deployed a non-coaxial elastoplastic constitutive model to explore the effect of non-coaxiality on silo phenomena. The non-coaxial FE modelling was performed on three problems: a simple shear test under various initial conditions, a steep hopper and a flat-bottomed silo. The results show that non-coaxiality did not influence the prediction of wall pressure during filling and storing, on the other hand, the discharge pressure was predicted to be larger when non-coaxiality is considered