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Transport Problems (transport + problem)
Selected AbstractsReplica Exchange Light TransportCOMPUTER GRAPHICS FORUM, Issue 8 2009Shinya Kitaoka I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism; I.3.3 [Computer Graphics]: Picture/Image Generation Abstract We solve the light transport problem by introducing a novel unbiased Monte Carlo algorithm called replica exchange light transport, inspired by the replica exchange Monte Carlo method in the fields of computational physics and statistical information processing. The replica exchange Monte Carlo method is a sampling technique whose operation resembles simulated annealing in optimization algorithms using a set of sampling distributions. We apply it to the solution of light transport integration by extending the probability density function of an integrand of the integration to a set of distributions. That set of distributions is composed of combinations of the path densities of different path generation types: uniform distributions in the integral domain, explicit and implicit paths in light (particle/photon) tracing, indirect paths in bidirectional path tracing, explicit and implicit paths in path tracing, and implicit caustics paths seen through specular surfaces including the delta function in path tracing. The replica-exchange light transport algorithm generates a sequence of path samples from each distribution and samples the simultaneous distribution of those distributions as a stationary distribution by using the Markov chain Monte Carlo method. Then the algorithm combines the obtained path samples from each distribution using multiple importance sampling. We compare the images generated with our algorithm to those generated with bidirectional path tracing and Metropolis light transport based on the primary sample space. Our proposing algorithm has better convergence property than bidirectional path tracing and the Metropolis light transport, and it is easy to implement by extending the Metropolis light transport. [source] Inversion of time-dependent nuclear well-logging data using neural networksGEOPHYSICAL PROSPECTING, Issue 1 2008Laura Carmine ABSTRACT The purpose of this work was to investigate a new and fast inversion methodology for the prediction of subsurface formation properties such as porosity, salinity and oil saturation, using time-dependent nuclear well logging data. Although the ultimate aim is to apply the technique to real-field data, an initial investigation as described in this paper, was first required; this has been carried out using simulation results from the time-dependent radiation transport problem within a borehole. Simulated neutron and ,-ray fluxes at two sodium iodide (NaI) detectors, one near and one far from a pulsed neutron source emitting at ,14 MeV, were used for the investigation. A total of 67 energy groups from the BUGLE96 cross section library together with 567 property combinations were employed for the original flux response generation, achieved by solving numerically the time-dependent Boltzmann radiation transport equation in its even parity form. Material property combinations (scenarios) and their correspondent teaching outputs (flux response at detectors) are used to train the Artificial Neural Networks (ANNs) and test data is used to assess the accuracy of the ANNs. The trained networks are then used to produce a surrogate model of the expensive, in terms of computational time and resources, forward model with which a simple inversion method is applied to calculate material properties from the time evolution of flux responses at the two detectors. The inversion technique uses a fast surrogate model comprising 8026 artificial neural networks, which consist of an input layer with three input units (neurons) for porosity, salinity and oil saturation; and two hidden layers and one output neuron representing the scalar photon or neutron flux prediction at the detector. This is the first time this technique has been applied to invert pulsed neutron logging tool information and the results produced are very promising. The next step in the procedure is to apply the methodology to real data. [source] Energy Group optimization for forward and inverse problems in nuclear engineering: application to downwell-logging problemsGEOPHYSICAL PROSPECTING, Issue 2 2006Elsa Aristodemou ABSTRACT Simulating radiation transport of neutral particles (neutrons and ,-ray photons) within subsurface formations has been an area of research in the nuclear well-logging community since the 1960s, with many researchers exploiting existing computational tools already available within the nuclear reactor community. Deterministic codes became a popular tool, with the radiation transport equation being solved using a discretization of phase-space of the problem (energy, angle, space and time). The energy discretization in such codes is based on the multigroup approximation, or equivalently the discrete finite-difference energy approximation. One of the uncertainties, therefore, of simulating radiation transport problems, has become the multigroup energy structure. The nuclear reactor community has tackled the problem by optimizing existing nuclear cross-sectional libraries using a variety of group-collapsing codes, whilst the nuclear well-logging community has relied, until now, on libraries used in the nuclear reactor community. However, although the utilization of such libraries has been extremely useful in the past, it has also become clear that a larger number of energy groups were available than was necessary for the well-logging problems. It was obvious, therefore, that a multigroup energy structure specific to the needs of the nuclear well-logging community needed to be established. This would have the benefit of reducing computational time (the ultimate aim of this work) for both the stochastic and deterministic calculations since computational time increases with the number of energy groups. We, therefore, present in this study two methodologies that enable the optimization of any multigroup neutron,, energy structure. Although we test our theoretical approaches on nuclear well-logging synthetic data, the methodologies can be applied to other radiation transport problems that use the multigroup energy approximation. The first approach considers the effect of collapsing the neutron groups by solving the forward transport problem directly using the deterministic code EVENT, and obtaining neutron and ,-ray fluxes deterministically for the different group-collapsing options. The best collapsing option is chosen as the one which minimizes the effect on the ,-ray spectrum. During this methodology, parallel processing is implemented to reduce computational times. The second approach uses the uncollapsed output from neural network simulations in order to estimate the new, collapsed fluxes for the different collapsing cases. Subsequently, an inversion technique is used which calculates the properties of the subsurface, based on the collapsed fluxes. The best collapsing option is chosen as the one that predicts the subsurface properties with a minimal error. The fundamental difference between the two methodologies relates to their effect on the generated ,-rays. The first methodology takes the generation of ,-rays fully into account by solving the transport equation directly. The second methodology assumes that the reduction of the neutron groups has no effect on the ,-ray fluxes. It does, however, utilize an inversion scheme to predict the subsurface properties reliably, and it looks at the effect of collapsing the neutron groups on these predictions. Although the second procedure is favoured because of (a) the speed with which a solution can be obtained and (b) the application of an inversion scheme, its results need to be validated against a physically more stringent methodology. A comparison of the two methodologies is therefore given. [source] Superconvergence and H(div) projection for discontinuous Galerkin methodsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2003Peter Bastian Abstract We introduce and analyse a projection of the discontinuous Galerkin (DG) velocity approximations that preserve the local mass conservation property. The projected velocities have the additional property of continuous normal component. Both theoretical and numerical convergence rates are obtained which show that the accuracy of the DG velocity field is maintained. Superconvergence properties of the DG methods are shown. Finally, numerical simulations of complicated flow and transport problem illustrate the benefits of the projection. Copyright © 2003 John Wiley & Sons, Ltd. [source] Adaptive approach for nonlinear sensitivity analysis of reaction kineticsJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 9 2005Illia Horenko Abstract We present a unified approach for linear and nonlinear sensitivity analysis for models of reaction kinetics that are stated in terms of systems of ordinary differential equations (ODEs). The approach is based on the reformulation of the ODE problem as a density transport problem described by a Fokker,Planck equation. The resulting multidimensional partial differential equation is herein solved by extending the TRAIL algorithm originally introduced by Horenko and Weiser in the context of molecular dynamics (J. Comp. Chem. 2003, 24, 1921) and discussed it in comparison with Monte Carlo techniques. The extended TRAIL approach is fully adaptive and easily allows to study the influence of nonlinear dynamical effects. We illustrate the scheme in application to an enzyme-substrate model problem for sensitivity analysis w.r.t. to initial concentrations and parameter values. © 2005 Wiley Periodicals, Inc. J Comput Chem 26: 941,948, 2005 [source] An implementation of radiative transfer in the cosmological simulation code gadgetMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 3 2009Margarita Petkova ABSTRACT We present a novel numerical implementation of radiative transfer in the cosmological smoothed particle hydrodynamics (SPH) simulation code gadget. It is based on a fast, robust and photon-conserving integration scheme where the radiation transport problem is approximated in terms of moments of the transfer equation and by using a variable Eddington tensor as a closure relation, following the Optically Thin Variable Eddington Tensor suggestion of Gnedin & Abel. We derive a suitable anisotropic diffusion operator for use in the SPH discretization of the local photon transport, and we combine this with an implicit solver that guarantees robustness and photon conservation. This entails a matrix inversion problem of a huge, sparsely populated matrix that is distributed in memory in our parallel code. We solve this task iteratively with a conjugate gradient scheme. Finally, to model photon sink processes we consider ionization and recombination processes of hydrogen, which is represented with a chemical network that is evolved with an implicit time integration scheme. We present several tests of our implementation, including single and multiple sources in static uniform density fields with and without temperature evolution, shadowing by a dense clump and multiple sources in a static cosmological density field. All tests agree quite well with analytical computations or with predictions from other radiative transfer codes, except for shadowing. However, unlike most other radiative transfer codes presently in use for studying re-ionization, our new method can be used on-the-fly during dynamical cosmological simulation, allowing simultaneous treatments of galaxy formation and the re-ionization process of the Universe. [source] Intraneuronal APP/A, Trafficking and Plaque Formation in ,-Amyloid Precursor Protein and Presenilin-1 Transgenic MiceBRAIN PATHOLOGY, Issue 3 2002Oliver Wirths Neuropil deposition of ,-amyloid peptides A,40 and A,42 is believed to be the key event in the neurodegenerative processes of Alzheimer's disease (AD). Since A, seems to carry a transport signal that is required for axonal sorting of its precursor ,-amyloid precursor protein (APP), we studied the intraneuronal staining profile of A, peptides in a transgenic mouse model expressing human mutant APP751 (KM670/671NL and V717I) and human mutant presenilin-1 (PS-1 M146L) in neurons. Using surface plasmon resonance we analyzed the A, antibodies and defined their binding profile to APP, A,40 and A,42. Immunohistochemical staining revealed that intraneuronal A,40 and A,42 staining preceded plaque deposition, which started at 3 months of age. A, was observed in the somatodendritic and axonal compartments of many neurons. Interestingly, the striatum, which lacks transgenic APP expression harbored many plaques at 10 months of age. This is most likely due to an APP/A, transport problem and may be a model region to study APP/A, trafficking as an early pathological event. [source] Growth of lead bromide polycrystalline filmsCRYSTAL RESEARCH AND TECHNOLOGY, Issue 10 2004M. Giles Abstract Lead bromide polycrystalline films were grown by the physical vapor deposition method (PVD). Glass 1,x1, in size, uncoated, and coated with Indium Tin Oxide (ITO), was used as substrate and rear contact. The starting material was evaporated at temperatures from 395°C to 530°C under high vacuum atmosphere (6 x 10 -3 Pa) and during 8 days. The substrate temperature was prefixed from 190°C to 220°C. Film thickness yielded values from 40 to 90 ,m. Optical microscopy and scanning electron microscopy (SEM) were performed on the films. Grain size resulted to be from 1.0 to 3.5 ,m. SEM and X-ray diffraction indicate that films grow with a preferred orientation with the (0 0 l) planes parallel to the substrate. The Texture Coefficient (TC) related to the plane (0 0 6) was 7.3. Resistivity values in the order of 1012 ,cm were obtained for the oriented samples, but a strong polarization indicates severe charge transport problems in the films. Film properties were correlated with the growth temperature and with previous results for films of other halides. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Modelling Approach for Planar Self-Breathing PEMFC and Comparison with Experimental Results,FUEL CELLS, Issue 4 2004A. Schmitz Abstract This paper presents a model-based analysis of a proton exchange membrane fuel cell,(PEMFC) with a planar design as the power supply for portable applications. The cell is operated with hydrogen and consists of an open cathode side allowing for passive, self-breathing, operation. This planar fuel cell is fabricated using printed circuit board,(PCB) technology. Long-term stability of this type of fuel cell has been demonstrated. A stationary, two-dimensional, isothermal, mathematical model of the planar fuel cell is developed. Fickian diffusion of the gaseous components,(O2, H2, H2O) in the gas diffusion layers and the catalyst layers is accounted for. The transport of water is considered in the gaseous phase only. The electrochemical reactions are described by the Tafel equation. The potential and current balance equations are solved separately for protons and electrons. The resulting system of partial differential equations is solved by a finite element method using FEMLAB,(COMSOL Inc.) software. Three different cathode opening ratios are realized and the corresponding polarization curves are measured. The measurements are compared to numerical simulation results. The model reproduces the shape of the measured polarization curves and comparable limiting current density values, due to mass transport limitation, are obtained. The simulated distribution of gaseous water shows that an increase of the water concentration under the rib occurs. It is concluded that liquid water may condense under the rib leading to a reduction of the open pore space accessible for gas transport. Thus, a broad rib not only hinders the oxygen supply itself, but may also cause additional mass transport problems due to the condensation of water. [source] Energy Group optimization for forward and inverse problems in nuclear engineering: application to downwell-logging problemsGEOPHYSICAL PROSPECTING, Issue 2 2006Elsa Aristodemou ABSTRACT Simulating radiation transport of neutral particles (neutrons and ,-ray photons) within subsurface formations has been an area of research in the nuclear well-logging community since the 1960s, with many researchers exploiting existing computational tools already available within the nuclear reactor community. Deterministic codes became a popular tool, with the radiation transport equation being solved using a discretization of phase-space of the problem (energy, angle, space and time). The energy discretization in such codes is based on the multigroup approximation, or equivalently the discrete finite-difference energy approximation. One of the uncertainties, therefore, of simulating radiation transport problems, has become the multigroup energy structure. The nuclear reactor community has tackled the problem by optimizing existing nuclear cross-sectional libraries using a variety of group-collapsing codes, whilst the nuclear well-logging community has relied, until now, on libraries used in the nuclear reactor community. However, although the utilization of such libraries has been extremely useful in the past, it has also become clear that a larger number of energy groups were available than was necessary for the well-logging problems. It was obvious, therefore, that a multigroup energy structure specific to the needs of the nuclear well-logging community needed to be established. This would have the benefit of reducing computational time (the ultimate aim of this work) for both the stochastic and deterministic calculations since computational time increases with the number of energy groups. We, therefore, present in this study two methodologies that enable the optimization of any multigroup neutron,, energy structure. Although we test our theoretical approaches on nuclear well-logging synthetic data, the methodologies can be applied to other radiation transport problems that use the multigroup energy approximation. The first approach considers the effect of collapsing the neutron groups by solving the forward transport problem directly using the deterministic code EVENT, and obtaining neutron and ,-ray fluxes deterministically for the different group-collapsing options. The best collapsing option is chosen as the one which minimizes the effect on the ,-ray spectrum. During this methodology, parallel processing is implemented to reduce computational times. The second approach uses the uncollapsed output from neural network simulations in order to estimate the new, collapsed fluxes for the different collapsing cases. Subsequently, an inversion technique is used which calculates the properties of the subsurface, based on the collapsed fluxes. The best collapsing option is chosen as the one that predicts the subsurface properties with a minimal error. The fundamental difference between the two methodologies relates to their effect on the generated ,-rays. The first methodology takes the generation of ,-rays fully into account by solving the transport equation directly. The second methodology assumes that the reduction of the neutron groups has no effect on the ,-ray fluxes. It does, however, utilize an inversion scheme to predict the subsurface properties reliably, and it looks at the effect of collapsing the neutron groups on these predictions. Although the second procedure is favoured because of (a) the speed with which a solution can be obtained and (b) the application of an inversion scheme, its results need to be validated against a physically more stringent methodology. A comparison of the two methodologies is therefore given. [source] Modelling of contaminant transport through landfill liners using EFGMINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 7 2010R. Praveen Kumar Abstract Modelling of contaminant transport through landfill liners and natural soil deposits is an important area of research activity in geoenvironmental engineering. Conventional mesh-based numerical methods depend on mesh/grid size and element connectivity and possess some difficulties when dealing with advection-dominant transport problems. In the present investigation, an attempt has been made to provide a simple but sufficiently accurate methodology for numerical simulation of the two-dimensional contaminant transport through the saturated homogeneous porous media and landfill liners using element-free Galerkin method (EFGM). In the EFGM, an approximate solution is constructed entirely in terms of a set of nodes and no characterization of the interrelationship of the nodes is needed. The EFGM employs moving least-square approximants to approximate the function and uses the Lagrange multiplier method for imposing essential boundary conditions. The results of the EFGM are validated using experimental results. Analytical and finite element solutions are also used to compare the results of the EFGM. In order to test the practical applicability and performance of the EFGM, three case studies of contaminant transport through the landfill liners are presented. A good agreement is obtained between the results of the EFGM and the field investigation data. Copyright © 2009 John Wiley & Sons, Ltd. [source] Investigation of a modified sequential iteration approach for solving coupled reactive transport problemsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 2 2006David J. Z. Chen Abstract When contaminants enter the soil or groundwater, they may interact physically, geochemically and biochemically with the native water, microorganisms and solid matrix. A realistic description of a reactive transport regime that includes these processes requires joint consideration of multiple chemical species. Currently there are three common numerical approaches for coupling multispecies reaction and solute transport: the one-step approach, the sequential non-iterative approach (SNIA), and the sequential iterative approach (SIA). A modification of the SNIA method is the Strang-splitting method. In this study, a new modified sequential iteration approach (MSIA) for solving multicomponent reactive transport in steady state groundwater flow is presented. This coupling approach has been applied to two realistic reactive transport problems and its performance compared with the SIA and the Strang-splitting methods. The comparison shows that MSIA consistently converges faster than the other two coupling schemes. For the simulation of nitrogen and related species transport and reaction in a riparian aquifer, the total CPU time required by MSIA is only about 38% of the total CPU time required by the SIA, and only 50% of the CPU time required by the Strang-splitting method. The test problem results indicate that the SIA has superior accuracy, while the accuracy of MSIA is marginally better than that of the Strang-splitting method. The overall performance of MSIA is considered to be good, especially for simulations in which computational time is a critical factor. Copyright © 2005 John Wiley & Sons, Ltd. [source] A higher-order predictor,corrector scheme for two-dimensional advection,diffusion equationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2008Chuanjian Man Abstract A higher-order accurate numerical scheme is developed to solve the two-dimensional advection,diffusion equation in a staggered-grid system. The first-order spatial derivatives are approximated by the fourth-order accurate finite-difference scheme, thus all truncation errors are kept to a smaller order of magnitude than those of the diffusion terms. Therefore, there is no need to add an artificial diffusion term to balance the unwanted numerical diffusion. For the time derivative, the fourth-order accurate Adams,Bashforth predictor,corrector method is applied. The stability analysis of the proposed scheme is carried out using the Von Neumann method. It is shown that the proposed algorithm has good stability. This method also shows much less spurious oscillations than current lower-order accurate numerical schemes. As a result, the proposed numerical scheme can provide more accurate results for long-time simulations. The proposed numerical scheme is validated against available analytical and numerical solutions for one- and two-dimensional transport problems. One- and two-dimensional numerical examples are presented in this paper to demonstrate the accuracy and conservative properties of the proposed algorithm by comparing with other numerical schemes. The proposed method is demonstrated to be a useful and accurate modelling tool for a wide range of transport problems. Copyright © 2007 John Wiley & Sons, Ltd. [source] Positivity-preserving, flux-limited finite-difference and finite-element methods for reactive transportINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2003Robert J. MacKinnon Abstract A new class of positivity-preserving, flux-limited finite-difference and Petrov,Galerkin (PG) finite-element methods are devised for reactive transport problems. The methods are similar to classical TVD flux-limited schemes with the main difference being that the flux-limiter constraint is designed to preserve positivity for problems involving diffusion and reaction. In the finite-element formulation, we also consider the effect of numerical quadrature in the lumped and consistent mass matrix forms on the positivity-preserving property. Analysis of the latter scheme shows that positivity-preserving solutions of the resulting difference equations can only be guaranteed if the flux-limited scheme is both implicit and satisfies an additional lower-bound condition on time-step size. We show that this condition also applies to standard Galerkin linear finite-element approximations to the linear diffusion equation. Numerical experiments are provided to demonstrate the behavior of the methods and confirm the theoretical conditions on time-step size, mesh spacing, and flux limiting for transport problems with and without nonlinear reaction. Copyright © 2003 John Wiley & Sons, Ltd. [source] On the use of large time steps with ELLAM for transport with kinetic reactions over heterogeneous domainsAICHE JOURNAL, Issue 5 2009Marwan Fahs Abstract An Eulerian Lagrangian localized adjoint method (ELLAM) is considered for the resolution of advection-dominated transport problems in porous media. Contrary to standard Eulerian methods, ELLAM can use large time steps because the advection term is approximated accurately without any CFL restriction. However, it is shown in this article that special care must be taken for the approximation of the dispersive and reactive terms when large time steps are used over heterogeneous domains. An alternative procedure is proposed. It is based on an equivalent dispersion coefficient or an equivalent reaction rate when different zones are encountered during the tracking. Numerical experiments are performed with variable dispersion or variable reaction rates over space (including nonlinearity). When classical ELLAM require numerous time steps to handle heterogeneity, the alternative procedure is shown to perform with the same accuracy in a single time step. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source] A monotonic and positive,definite filter for a Semi-Lagrangian Inherently Conserving and Efficient (SLICE) schemeTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 611 2005Mohamed Zerroukat Abstract A new monotonic and positive,definite filter is incorporated into an existing Semi-Lagrangian Inherently Conserving and Efficient (SLICE) scheme for transport problems in both Cartesian and spherical geometry. The SLICE scheme is based on a control-volume approach that uses multiple sweeps of a one-dimensional O (,x4) conservation remapping algorithm along predetermined cascade directions. The new filter combines a selective detection algorithm, to pinpoint regions of non-monotonic behaviour, with a hierarchical reduction of the degree of the piecewise reconstruction in such regions, to re-establish monotonicity. The enhanced, monotonic and positive,definite, SLICE scheme is tested in one dimension, and then applied to standard two-dimensional test problems in both Cartesian and spherical geometries. Comparisons with published results of other conservative semi-Lagrangian schemes show that it performs well. © Crown copyright, 2005. [source] SLICE-S: A Semi-Lagrangian Inherently Conserving and Efficient scheme for transport problems on the SphereTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 602 2004Mohamed Zerroukat Abstract The Semi-Lagrangian Inherently Conserving and Efficient (SLICE) scheme developed for Cartesian geometry is generalized to spherical geometry. The spherical version, SLICE-S, is similarly based on a Control Volume approach and multiple sweeps of a one-dimensional O(,s4) (where s is the spherical distance) conservative remapping algorithm along Eulerian latitudes, then along Lagrangian longitudes. The resulting conservative scheme requires no restriction on either the polar meridional or zonal Courant numbers. SLICE-S is applied to the standard problems of solid-body rotation and deformational flow, and results are compared with those of a standard non-conservative and other published conservative semi-Lagrangian schemes. In addition to mass conservation, and consistent with the performance of SLICE, the present scheme is competitive in terms of accuracy and efficiency. © Crown copyright, 2004. Royal Meteorological Society [source] | ||||||||||||||||||||||