Numerical performance of incomplete factorizations for 3D transient convection-diffusion problems

Many environmental processes can be modelled as transient convection–diffusion–reaction problems. This is the case, for instance, of the operation of activated-carbon filters. For industrial applications there is a growing demand for 3D simulations, so efficient linear solvers are a major concern. We have compared the numerical performance of two families of incomplete Cholesky factorizations as preconditioners of conjugate gradient iterations: drop-tolerance and prescribed-memory strategies. Numerical examples show that the former are computationally more efficient, but the latter may be preferable due to their predictable memory requirements.Peer ReviewedPostprint (author’s final draft

Analysis of Convection-Diffusion Problems at Various Peclet Numbers Using Finite Volume and Finite Difference Schemes

Convection-diffusion problems arise frequently in many areas of applied sciences and engineering. In this paper, we solve a convection-diffusion problem by central differencing scheme, upwinding differencing scheme (which are special cases of finite volume scheme) and finite difference scheme at various Peclet numbers. It is observed that when central differencing scheme is applied, the solution changes rapidly at high Peclet number because when velocity is large, the flow term becomes large, and the convection term dominates. Similarly, when velocity is low, the diffusion term dominates and the solution diverges, i.e., mathematically the system does not satisfy the criteria of consistency. On applying upwinding differencing scheme, we conclude that the criteria of consistency is satisfied because in this scheme the flow direction is also considered. To support our study, a test example is taken and comparison of the numerical solutions with the analytical solutions is done. Keywords: Finite volume method, Partial differential equation

Three-dimensional finite element modelling of stack pollutant emissions

In this paper we propose a finite element method approach formodelling the air quality in a local scale over complex terrain. The area of interest is up to tens of kilometres and it includes pollutant sources. The proposed methodology involves the generation of an adaptive tetrahedral mesh, the computation of an ambient wind field, the inclusion of the plume rise effect in the wind field, and the simulation of transport and reaction of pollutants. The methodology is used to simulate a fictitious pollution episode in La Palma island (Canary Island, Spain).Peer ReviewedPostprint (published version

Insertion of triangulated surfaces into a meccano tetrahedral discretization by means of mesh refinement and optimization procedures

This is the peer reviewed version of the following article: Ruiz Gironès , E., Oliver , A., Socorro, G., Cascón, J., Escobar, J.M., Montenegro, R., Sarrate, J. Insertion of triangulated surfaces into a meccano tetrahedral discretization by means of mesh refinement and optimization procedures. "International journal for numerical methods in engineering", 2018, which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nme.5706/pdf. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.In this paper, we present a new method for inserting several triangulated surfaces into an existing tetrahedral mesh generated by the meccano method. The result is a conformal mesh where each inserted surface is approximated by a set of faces of the final tetrahedral mesh. First, the tetrahedral mesh is refined around the inserted surfaces to capture their geometric features. Second, each immersed surface is approximated by a set of faces from the tetrahedral mesh. Third, following a novel approach, the nodes of the approximated surfaces are mapped to the corresponding immersed surface. Fourth, we untangle and smooth the mesh by optimizing a regularized shape distortion measure for tetrahedral elements in which we move all the nodes of the mesh, restricting the movement of the edge and surface nodes along the corresponding entity they belong to. The refining process allows approximating the immersed surface for any initial meccano tetrahedral mesh. Moreover, the proposed projection method avoids computational expensive geometric projections. Finally, the applied simultaneous untangling and smoothing process delivers a high-quality mesh and ensures that the immersed surfaces are interpolated. Several examples are presented to assess the properties of the proposed method.Peer ReviewedPostprint (author's final draft

Simulating large emitters using CMAQ and a local scale finite element model: analysis of the surroundings of Barcelona

In this work, we present a novel approach to simulate large emitters in the microscale. The main idea is to combine a nested grid approach and a finite element model to simulate the subgrid scale. The nested grid system consists of the mesoscale meteorological model WRF-ARW, the Air Emission Model of Meteosim (AEMM), and the air quality model CMAQ. The subgrid scale is simulated using an adaptive, Eulerian, non-steady finite element model. The results from the nested grid simulation are used as initial and boundary conditions in the subgrid model, making this approach one-way. A simulation has been carried out in the surroundings of Barcelona, where an important contributor to the sulphur dioxide levels is considered. The simulations were carried out for one episode with high levels of sulphur dioxide. The time period of the simulation was 48 hours with a 24-hour spin-up.Peer ReviewedPostprint (author's final draft

Моделі процесів дифузійного переносу і методи оцінювання параметрів в багатокомпозитних наноплівках : Монографія

В монографії представлені математичні моделі фізико-технологічних процесів перенесення в багатошарових плівках декартового та циліндричного типу, моделі дифузійного переносу в багатошарових оксидних та Fe/Tb, Dy/Fe - магнітних наноплівках різної конфігурації з урахуванням взаємодій між окремими шарами плівок. Наведено результати комп’ютерного моделювання та аналіз концентраційних залежностей дифундованих компонентів у шарах наноплівок як функцій від товщини для різних зрізів технологічних поверхонь, що дає можливість їх подальшого використання для комплексної оцінки ресурсозбереження, зокрема показників корозійностійкості та жаростійкості оксидних плівок при виробництві тонких скловолокон.Для наукових працівників, фахівців у галузі прикладної математики, математичного моделювання, програмної інженерії, викладачів вищих навчальних закладів, аспірантів, інженерів та студентів, що цікавляться питаннями створення програмного забезпечення для моделювання та ідентифікації масопереносу в нанопористих середовищах та суміжними напрямами

Моделі процесів дифузійного переносу і методи оцінювання параметрів в багато композитних наноплівках

В монографії представлені математичні моделі фізико-технологічних процесів перенесення в багатошарових плівках декартового та циліндричного типу, моделі дифузійного переносу в багатошарових оксидних та Fe/Tb, Dy/Fe - магнітних наноплівках різної конфігурації з урахуванням взаємодій між окремими шарами плівок. Наведено результати комп’ютерного моделювання та аналіз концентраційних залежностей дифундованих компонентів у шарах наноплівок як функцій від товщини для різних зрізів технологічних поверхонь, що дає можливість їх подальшого використання для комплексної оцінки ресурсозбереження, зокрема показників корозійностійкості та жаростійкості оксидних плівок при виробництві тонких скловолокон

Numerical performance of incomplete factorizations for 3D transient convection-diffusion problems

Many environmental processes can be modelled as transient convection–diffusion–reaction problems. This is the case, for instance, of the operation of activated-carbon filters. For industrial applications there is a growing demand for 3D simulations, so efficient linear solvers are a major concern. We have compared the numerical performance of two families of incomplete Cholesky factorizations as preconditioners of conjugate gradient iterations: drop-tolerance and prescribed-memory strategies. Numerical examples show that the former are computationally more efficient, but the latter may be preferable due to their predictable memory requirements.Peer Reviewe

Local scale air quality model system for diagnostic and forecasting simulations using the finite element method

Air pollution is an important topic with a great social impact; it is related with public health, environment and ecology, and climate change. Scientists have developed several models in the last thirty years, and regional air quality operational systems are used routinely by governments and agencies. Efforts have also been done to simulate the air quality in the local scale; main models are Gaussian and Puff models, that are based on a Lagrangian approach. In contrast with these models, in this thesis we have developed a system using an Eulerian approach. This model is specifically designed for regions with complex orography where the Lagrangian models have problems computing the trajectory of the particles. This model can be used for diagnostic or prediction simulations. Air quality operational systems depend on the orography, meteorological data, and emission data. Air quality models use processors to incorporate these data into the model. The data can come from numerical weather prediction systems, experimental data, or databases. In this thesis we have developed processors, specifically designed for the local scale, to incorporate these data into our system. To incorporate the orography, we have developed a mesh generation algorithm suitable for complex terrain discretization; it also allows to insert layers that can match the regional models. A wind field model has also been used; it can interpolate a three-dimensional wind field from some station measurements using a log-linear vertical wind profile, or can interpolate it from a numerical weather prediction system. Once an interpolated wind field is computed, a mass-consistent model is applied to ensure null divergence and impermeability in the terrain. The wind field is modified to take into account the injection of the pollutants into the atmosphere. Briggs studied the trajectory of the plume rise giving some empirical equations that will be used in our model. Briggs' equations describe the trajectory in a plane; our model will modify this trajectory adapting it to the ambient wind field. This modification allows the plume rise to surround the mountains or channel into the valleys. The transport and reaction of pollutants in the atmosphere is then computed using an splitting method, so the transport and the chemical reactions are computed independently. To solve the transport of pollutants we have used a finite element method stabilized using least squares. The chemical reaction is simulated using simplified models such as RIVAD, or more complex ones such as CB05. To obtain more accurate results we have used adaptation. An error indicator has been used to adapt the mesh to the solution. To adapt the mesh to the concentration distribution of all the species is very demanding, for this reason we have used a multimesh method where every chemical specie has its own mesh where we solve the transport and the chemical reactions are simulated in a common mesh. The system developed in this thesis has diagnostic and forecasting capabilities. For this reason we present two different applications. The first one is a diagnostic application in La Palma island (Spain), where wind measurements are given, and SO2 and NO2 emissions from a stack are considered. The topography of the island is real, from a digital elevation model, but the wind field measurements, and the stack location and emissions, are simulated. The second application is a forecasting application data from the CMAQ benchmark test. It is located in the surrounding of Pineville Kentucky. In this application we have used all the data from CMAQ and the chemical reaction model CB05.La contaminació atmosfèrica té gran impacte social; està relacionada ambla salut pública, l'ecologia, el medi ambient i el canvi climàtic. En els últims trenta anys, els científics han desenvolupat diversos models que els governs i les agències mediambientals utilitzen diàriament. També s'han fet esforços per simular la qualitat de l'aire en l'escala local. Els models principals són els models Gaussians i Puff, que es basen en una descripció Lagrangiana. En contrast amb aquests models, en aquesta tesi s'ha desenvolupat un sistema que utilitza una descripció Euleriana. Aquest model està dissenyat específicament per a les regions amb topografia complexa on els models Lagrangians tenen problemes calculant la trajectòria de les partícules. El model presentat en aquesta tesi pot ser utilitzat tant pel diagnòstic com per la predicció. Els sistemes operatius utilitzats actualment depenen de l'orografia, de dades meteorològiques i de dades d'emissió. Per tal d'incorporar aquestes dades, els models de qualitat de l'aire han desenvolupat diferents preprocessadors. Les dades poden venir dels sistemes numèrics de predicció meteorològics, de dades experimentals o de bases de dades. En aquesta tesi hem desenvolupat preprocessadors dissenyats específicament per a l'àmbit local, per tal d'incorporar aquestes dades al nostre sistema. Per incorporar l'orografia, hem desenvolupat un algoritme de generació de malles adequat per terreny complex; l'algoritme també ens permet inserir capes que poden coincidir amb la dels models regionals. S'ha desenvolupat un model de càlcul de camp de vent; a partir de les dades s'interpola un camp de vent tridimensional fent servir un perfil log-lineal vertical del vent, o s'interpola a partir dels resultats d'un sistema de predicció meteorològica. Quan s'ha calculat el vent interpolat, es fa servir un model de massa consistent per obtenir un camp de vent definitiu on s'ha imposat divergència zero i impermeabilitat del terreny. El camp de vent s'ha de modificar per tenir en compte la injecció dels contaminants a l'atmosfera. Briggs va estudiar la trajectòria de l'elevació de la ploma i va trobar equacions empíriques que utilitzarem en el nostre model. Les equacions de Briggs descriuen la trajectòria de la ploma en un pla vertical; el nostre model modificarà aquesta trajectòria adaptant-la al camp de vent ambiental. Aquesta modificació permet que l'elevació de la ploma rodegi les muntanyes o s'acanali a les valls. El transport i la reacció de contaminants a l'atmosfera es calcula utilitzant un mètode de "splitting", de manera que el transport i la reacció química es calculen de forma independent. Per resoldre el transport de contaminants, hem utilitzat el mètode d'elements finits estabilitzat amb mínims quadrats. La reacció química es simula mitjançant models simplificats com el model RIVAD, o més complexes com el CB05. Per obtenir resultats més precisos hem adaptat la malla a la solució utilitzant un indicador d'error. Haver d'adaptar la malla a la distribució de la concentració de totes les espècies contaminants és molt exigent i per aquest motiu hem utilitzat un mètode "multimesh" on cada espècie química té la seva pròpia malla on resolem el transport i les reaccions químiques es simulen en una malla comú. El sistema desenvolupat en aquesta tesi té capacitats de diagnòstic i pronòstic. Per aquesta raó es presenten dues aplicacions diferents. La primera és una aplicació de diagnòstic a l'illa de la Palma (Espanya), on es disposa de mesures de vent, i de les emissions de SO2 i NO2 d'una xemeneia. La topografia de l'illa és real, a partir d'un model digital del terreny, però les dades del camp de vent, la ubicació de la xemeneia i el valor de les emissions són simulades. La segona aplicació és una aplicació de predicció fent servir els resultats del benchmark del CMAQ. Es simula una zona a Pineville Kentucky. En aquesta aplicació hem utilitzat totes les dades del CMAQ i el model químic CB05