Short Time Steps Research Articles

Observations and 3D hydrodynamics-based modeling of decadal-scale shoreline change along the Outer Banks, North Carolina

Long-term decadal-scale shoreline change is an important parameter for quantifying the stability of coastal systems. The decadal-scale coastal change is controlled by processes that occur on short time scales (such as storms) and long-term processes (such as prevailing waves). The ability to predict decadal-scale shoreline change is not well established and the fundamental physical processes controlling this change are not well understood. Here we investigate the processes that create large-scale long-term shoreline change along the Outer Banks of North Carolina, an uninterrupted 60km stretch of coastline, using both observations and a numerical modeling approach. Shoreline positions for a 24-yr period were derived from aerial photographs of the Outer Banks. Analysis of the shoreline position data showed that, although variable, the shoreline eroded an average of 1.5m/yr throughout this period. The modeling approach uses a three-dimensional hydrodynamics-based numerical model coupled to a spectral wave model and simulates the full 24-yr time period on a spatial grid running on a short (second scale) time-step to compute the sediment transport patterns. The observations and the model results show similar magnitudes (O(105m3/yr)) and patterns of alongshore sediment fluxes. Both the observed and the modeled alongshore sediment transport rates have more rapid changes at the north of our section due to continuously curving coastline, and possible effects of alongshore variations in shelf bathymetry. The southern section with a relatively uniform orientation, on the other hand, has less rapid transport rate changes. Alongshore gradients of the modeled sediment fluxes are translated into shoreline change rates that have agreement in some locations but vary in others. Differences between observations and model results are potentially influenced by geologic framework processes not included in the model. Both the observations and the model results show higher rates of erosion (∼−1m/yr) averaged over the northern half of the section as compared to the southern half where the observed and modeled averaged net shoreline changes are smaller (<0.1m/yr). The model indicates accretion in some shallow embayments, whereas observations indicate erosion in these locations. Further analysis identifies that the magnitude of net alongshore sediment transport is strongly dominated by events associated with high wave energy. However, both big- and small- wave events cause shoreline change of the same order of magnitude because it is the gradients in transport, not the magnitude, that are controlling shoreline change. Results also indicate that alongshore momentum is not a simple balance between wave breaking and bottom stress, but also includes processes of horizontal vortex force, horizontal advection and pressure gradient that contribute to long-term alongshore sediment transport. As a comparison to a more simple approach, an empirical formulation for alongshore sediment transport is used. The empirical estimates capture the effect of the breaking term in the hydrodynamics-based model, however, other processes that are accounted for in the hydrodynamics-based model improve the agreement with the observed alongshore sediment transport.

Smoldyn: particle-based simulation with rule-based modeling, improved molecular interaction and a library interface.

Smoldyn is a spatial and stochastic biochemical simulator. It treats each molecule of interest as an individual particle in continuous space, simulating molecular diffusion, molecule-membrane interactions and chemical reactions, all with good accuracy. This article presents several new features. Smoldyn now supports two types of rule-based modeling. These are a wildcard method, which is very convenient, and the BioNetGen package with extensions for spatial simulation, which is better for complicated models. Smoldyn also includes new algorithms for simulating the diffusion of surface-bound molecules and molecules with excluded volume. Both are exact in the limit of short time steps and reasonably good with longer steps. In addition, Smoldyn supports single-molecule tracking simulations. Finally, the Smoldyn source code can be accessed through a C/C ++ language library interface. Smoldyn software, documentation, code, and examples are at http://www.smoldyn.org . steven.s.andrews@gmail.com.

Surface temperature of carbon composite samples during thermal degradation

An infrared camera and a Fourier transform infrared spectrometer were used simultaneously to observe the radiation from the surface of carbon composite samples during thermal degradation experiments. Surface temperatures were estimated from radiation measurements conducted during cone calorimeter tests. Infrared spectra and images were post-processed involving a subtraction method between successive images, to withdraw the high incident flux from the cone calorimeter partly reflected by the sample. The surface intensities were first evaluated as a function of time. Then, an identification step was implemented linking the rise in intensity between two time steps with the increase in sample temperature. Corrections were introduced for the reflection of the incident radiation from the heater and for the true emissivity of the material. Both experimental devices – camera and spectrometer – showed temperature evolutions in a good agreement. The sharp temperature increase of the sample and the auto-ignition of the pyrolysis gases on the surface were observed and evaluated for various incident fluxes from the cone between 20 and 65 kW/m2. Measurements carried out with a short time step down to 0.2 s further allowed an evaluation of the supplementary flux due to the auto-ignition with a peak up to 20 kW/m2 for an incident flux of 35 kW/m2 on a carbon composite sample with surface 50 mm × 300 mm and thickness 5 mm.

An accurate interest matching algorithm based on prediction of the space–time intersection of regions for the distributed virtual environment

Interest matching is an important data-filtering mechanism for a large-scale distributed virtual environment. Many of the existing algorithms perform interest matching at discrete timesteps. Thus, they may suffer the missing-event problem: failing to report the events between two consecutive timesteps. Some algorithms solve this problem, by setting short timesteps, but they have a low computing efficiency. Additionally, these algorithms cannot capture all events, and some spurious events may also be reported. In this paper, we present an accurate interest matching algorithm called the predictive interest matching algorithm, which is able to capture the missing events between discrete timesteps. The PIM algorithm exploits the polynomial functions to model the movements of virtual entities, and predict the time intervals of region overlaps associated with the entities accurately. Based on the prediction of the space–time intersection of regions, our algorithm can capture all missing events and does not report the spurious events at the same time. To improve the runtime performance, a technique called region pruning is proposed and used in our algorithm. In experiments, we compare the new algorithm with the frequent interest matching algorithm and the space–time interest matching algorithm on the HLA/RTI distributed infrastructure. The results prove that although an additional matching effort is required in the new algorithm, it outperforms the baselines in terms of event-capturing ability, redundant matching avoidance, runtime efficiency and scalability.

Effect of borehole short-time-step performance on long-term dynamic simulation of ground-source heat pump system

Despite many studies that were found in the literature regarding the modelling of the short-time-step (STS) behaviour of the borehole ground heat exchangers, reported investigations of its effect on the long-term dynamic simulation of a ground-source heat pump (GSHP) system were sparse. Hence, in this study, the dynamic performances of a GSHP system applied to an office zone in Hong Kong over a period of 10 years were compared with both the long-time-step (LTS) and STS approaches for the boreholes. It was found that with the adoption of the more appropriate STS approach, the simulated fluid temperature leaving the ground heat exchanger borefield was lower by at most 1.62°C over a range of ground and grout thermal conductivities investigated. This also allowed the design borehole length to be reduced by at most 14.4% while the resulting energy consumption was still better than those based on the LTS approach. In this regard, the STS approach should be employed in the long-term dynamic simulation of GSHP systems.

Combining stable isotopes, Eddy Covariance system and meteorological measurements for partitioning evapotranspiration, of winter wheat, into soil evaporation and plant transpiration in a semi-arid region

A good knowledge of the partitioning of evapotranspiration (ET) is particularly important for improving crop water productivity, especially in semi-arid regions where irrigated agriculture uses up to 85% of total available water. In this paper, stable isotopic method and micrometeorological data were combined to assess the ET partition into plant transpiration and soil evaporation of an irrigated winter wheat field lying in the center of Morocco characterized by a semi-arid climate. Atmospheric, vegetation and soil samples were collected during two consecutive growing seasons (2011–2012 and 2012–2013). The sampling campaign was carried out after and before two irrigation events and lasted for five days.Additionally, an Eddy covariance system and a standard meteorological station were installed. Isotope turbulent mixing relationships, isotopic values of transpired water from plants (T) and that of evaporating water vapor from soil surface (E) were used to estimate fractions of transpiration and evaporation contributing to the total ET. The partition of ET was only performed by using δ2H. In fact, results obtained during 2011–2012 period, showed that this method worked well for the deuterium in comparison to oxygen-18 (δ18O). After irrigation, the ratios T/ET were about 0.73, 0.59 and 0.74 respectively in Days Of Year (DOY) 53, 54 and 55, averaging 0.69. Prior to irrigation, when the soil was dry, the T/ET ratio was 0.83 and 0.77, respectively in two days (DOY 101 and 102), averaging 0.80. Afterward, these fractions have been used in conjunction with Eddy Covariance measurements for converting the obtained percentages to mmd−1 values which are required by the farmers and the water managers. The obtained averages of evaporation and transpiration were respectively: 1.76 and 3.85mmd−1 for the 2011–2012 and 1.34 and5.45mmd−1for the 2012–2013. Our approach is useful for partitioning ET in an irrigated winter wheat under semi-arid climate at an ecosystem scale on short time steps.

Estimation of the water quality of a large urbanized river as defined by the European WFD: what is the optimal sampling frequency?

Assessment of the quality of freshwater bodies is essential to determine the impact of human activities on water resources. The water quality status is estimated by comparing indicators with standard thresholds. Indicators are usually statistical criteria that are calculated on discrete measurements of water quality variables. If the time step of the measured time series is not sufficient to fully capture the variable’s variability, the deduced indicator may not reflect the system’s functioning. The goal of the present work is to assess, through a hydro-biogeochemical modeling approach, the optimal sampling frequency for an accurate estimation of 6 water quality indicators defined by the European Water Framework Directive (WFD) in a large human-impacted river, which receives large urban effluents (the Seine River across the Paris urban area). The optimal frequency depends on the sampling location and on the monitored variable. For fast varying compounds that originate from urban effluents, such as PO_{4}^{3-}, NH_{4}^{+} and NO_{2}^{-}, a sampling time step of one week or less is necessary. To be able to reflect the highly transient character of bloom events, chl a concentrations also require a short monitoring time step. On the contrary, for variables that exert high seasonal variability, as NO_{3}^{-} and O 2, monthly sampling can be sufficient for an accurate estimation of WFD indicators in locations far enough from major effluents. Integrative water quality variables, such as O 2, can be highly sensitive to hydrological conditions. It would therefore be relevant to assess the quality of water bodies at a seasonal scale rather than at annual or pluri-annual scales. This study points out the possibility to develop smarter monitoring systems by coupling both time adaptative automated monitoring networks and modeling tools used as spatio-temporal interpolators.

A Tale of Two Forest Carbon Assessments in the Eastern United States: Forest Use Versus Cover as a Metric of Change

The dynamics of land-use practices (for example, forest versus settlements) is often a major driver of changes in terrestrial carbon (C). As the management and conservation of forest land uses are considered a means of reducing future atmospheric CO2 concentrations, the monitoring of forest C stocks and stock change by categories of land-use change (for example, croplands converted to forest) is often a requirement of C monitoring protocols such as those espoused by the Intergovernmental Panel on Climate Change (that is, Good Practice Guidance and Guidelines). The identification of land use is often along a spectrum ranging from direct observation (for example, interpretation of owner intent via field visits) to interpretation of remotely sensed imagery (for example, land cover mapping) or some combination thereof. Given the potential for substantial differences across this spectrum of monitoring techniques, a region-wide, repeated forest inventory across the eastern U.S. was used to evaluate relationships between forest land-use change (derived from a forest inventory) and forest cover change (derived from Landsat modeling) in the context of forest C monitoring strategies. It was found that the correlation between forest land-use change and cover change was minimal (<0.08), with an increase in forest land use but a net decrease in forest cover being the most frequent observation. Cover assessments may be more sensitive to active forest management and/or conversion activities that can lead to confounded conclusions regarding the forest C sink (for example, decreasing forest cover but increasing C stocks in industrial timberlands). In contrast, the categorical nature of direct land-use field observations reduces their sensitivity to forest management activities (for example, clearcutting versus thinning) and recent disturbance events (for example, floods or wildfire) that may obscure interpretation of C dynamics over short time steps. While using direct land-use observations or cover mapping in forest C assessments, they should not be considered interchangeable as both approaches possess idiosyncratic qualities that should be considered when developing conclusions regarding forest C attributes and dynamics across large scales.

Multibody Modelling of Wave Energy Converters Using Pseudo-Spectral Methods With Application to a Three-Body Hinge-Barge Device

Multibody wave energy converters are composed of several bodies interconnected by joints. Two different formulations are adopted to describe the dynamics of multibody systems: the differential and algebraic equations (DAEs) formulation, and the ordinary differential equations (ODEs) formulation. While the number of variables required for the description of the dynamics of a multibody system is greater in the DAE formulation than in the ODE formulation, the ODE formulation involves an extra computational effort in order to describe the dynamics of the system with a smaller number of variables. In this paper, pseudo-spectral (PS) methods are applied in order to solve the dynamics of multibody wave energy converters using both DAE and ODE formulations. Apart from providing a solution to the dynamics of multibody systems, pseudo-spectral methods provide an accurate and efficient formulation for the control of multibody wave energy converters. As an application example, this paper focuses on the dynamic modeling of a three-body hinge-barge device, where wave-tank tests are carried out in order to validate the DAE and ODE models against experimental data. Comparison of the ODE and DAE PS methods against a reference model based on the straightforward (Runge-Kutta) integration of the equations of motion shows that pseudo-spectral methods are computationally more stable and require less computational effort for short time steps.

On the use of mass scaling for stable and efficient simulated tempering with molecular dynamics.

Simulated tempering (ST) is a generalized-ensemble algorithm that employs trajectories exploring a range of temperatures to effectively sample rugged energy landscapes. When implemented using the molecular dynamics method, ST can require the use of short time steps for ensuring the stability of trajectories at high temperatures. To address this shortcoming, a mass-scaling ST (MSST) method is presented in which the particle mass is scaled in proportion to the temperature. Mass scaling in the MSST method leads to velocity distributions that are independent of temperature and eliminates the need for velocity scaling after the accepted temperature updates that are required in conventional ST simulations. The homogeneity in time scales with changing temperature improves the stability of simulations and allows for the use of longer time steps at high temperatures. As a result, the MSST is found to be more efficient than the standard ST method, particularly for cases in which a large temperature range is employed. © 2016 Wiley Periodicals, Inc.

Impact of temporal resolution of inputs on hydrological model performance: An analysis based on 2400 flood events

Summary Hydro-climatic data at short time steps are considered essential to model the rainfall–runoff relationship, especially for short-duration hydrological events, typically flash floods. Also, using fine time step information may be beneficial when using or analysing model outputs at larger aggregated time scales. However, the actual gain in prediction efficiency using short time-step data is not well understood or quantified. In this paper, we investigate the extent to which the performance of hydrological modelling is improved by short time-step data, using a large set of 240 French catchments, for which 2400 flood events were selected. Six-minute rain gauge data were available and the GR4 rainfall–runoff model was run with precipitation inputs at eight different time steps ranging from 6 min to 1 day. Then model outputs were aggregated at seven different reference time scales ranging from sub-hourly to daily for a comparative evaluation of simulations at different target time steps. Three classes of model performance behaviour were found for the 240 test catchments: (i) significant improvement of performance with shorter time steps; (ii) performance insensitivity to the modelling time step; (iii) performance degradation as the time step becomes shorter. The differences between these groups were analysed based on a number of catchment and event characteristics. A statistical test highlighted the most influential explanatory variables for model performance evolution at different time steps, including flow auto-correlation, flood and storm duration, flood hydrograph peakedness, rainfall–runoff lag time and precipitation temporal variability.

Effects of hysteresis, rainfall dynamics, and temporal resolution of rainfall input data in solute transport modelling in uncropped soil

ABSTRACTNumerical simulations were carried out using the HYDRUS 1D model for three different types of uncropped soils. Input data were observed of rainfall during a 15-year period at three sites in Sweden. Simulations were run with and without consideration of hysteresis. Three different rainfall input time steps were used: 0.5, 4, and 24 h. Solute transport was evaluated using the centre of mass (zCOM) of breakthrough curves (BTCs) and largest depth where a pre-defined limit concentration was exceeded (zLC). Results showed that hysteretic flow was slower as compared to the non-hysteretic case. Results also showed that zCOM generally had a positive correlation with the number of high-intensity rainfalls and that the correlations were higher for the non-hysteretic case. The results show that it is important to use a sufficiently short rainfall input time step and an accurate description of the soil hysteresis when assessing the effects of a future higher-intensive rainfall climate with longer dry periods.Editor D. Koutsoyiannis; Associate editor D. Yang

Scenario-based comparative assessment of potential future electricity systems – A new methodological approach using Germany in 2050 as an example

In this paper a new method for the evaluation and comparison of potential future electricity systems is presented. The German electricity system in the year 2050 is used as an example. Based on a comprehensive scenario analysis defining a corridor for possible shares of fluctuating renewable energy sources (FRES) residual loads are calculated in a unified manner. The share of electricity from PV and wind power plants in Germany in the year 2050 is in a range of 42–122% and the load demand has a bandwidth of around 460–750TWh. The residual loads are input for an algorithm that defines a supplementary mix of technologies providing flexibility to the system. The overall system layout guarantees the balance of generation and demand at all times. Due to the fact that the same method for residual load calculation and mixture of technologies is applied for all scenarios, a good comparability is guaranteed and we are able to identify key characteristics for future developments. The unique feature of the new algorithms presented here is the very fast calculation for a year-long simulation with hourly or shorter time steps taking into account the state of charge or availability of all storage and flexibility technologies. This allows an analysis of many different scenarios on a macro-economic level, variation of input parameters can easily be done, and extensive sensitivity analysis is possible. Furthermore different shares of FRES, CO2-emission targets, interest rates or social acceptance of certain technologies can be included. The capabilities of the method are demonstrated by an analysis of potential German power system layouts with a base scenario of 90% CO2-reduction target compared to 1990 and by the identification of different options for a power sector with a high degree of decarbonisation. The approach also aims at a very high level of transparency both regarding the algorithms and regarding the input parameters of the different technologies taken into account. Therefore this paper also gives a comprehensive and complete overview on the technology parameters used. The forecast on all technologies for the year 2050 regarding technical and economic parameters was made in a comprehensive consultation process with more than 100 experts representing academia and industry working on all different technologies. An extensive analysis of options for the design of potential German energy supply systems in 2050 based on the presented methodology will be published in a follow-up paper.

Generalized model-based predictive weather control for the control of free cooling by enhanced night-time ventilation

Free cooling by enhanced night-time ventilation could be an efficient technique for decreasing the energy demand for the cooling of buildings. Such systems use the ambient cold of surrounding air, which is transported into buildings by mechanical fan-driven ventilation systems. Only carefully designed and operated systems can be efficient enough to compete with other free-cooling techniques, such as evaporative cooling or even compressor-driven mechanical cooling systems. The efficiency of free cooling by enhanced night-time ventilation could be significantly improved if a model-based predictive weather control algorithm is used for operation control. The aim of this article is to present a generalized model-based predictive weather control (G-MPWC) algorithm that was developed with a detailed short time step numerical simulation of the thermal response of the building and free cooling system and simplified weather forecast data. The result of the G-MWPC is a set of control matrixes that includes data on the forecast required night-time air exchange rate and forecast daily coefficient of the performance of the free cooling system regarding the forecast daily average ambient air temperature and amplitude and the pre-set free cooling system on/off temperature difference. An additional matrix that includes data on forecast maximum indoor air temperature is developed for the case of the free cooling system being unable to fulfil pre-set thermal comfort requirements. A unique set of G-MWPS control matrixes must be developed for specific buildings and building operation conditions; afterwards, that control matrix can be used for the predicted controlling of the free cooling system by night time ventilation for the whole range of summer time meteorological conditions. In this article, the method and numerical model for developing a G-MPWC algorithm is presented as well as an example of a control matrix developed for a typical office room. The G-MPWC algorithm was validated for the case of a free-cooled office room.

A new method for calculation of short time-step g-functions of vertical ground heat exchangers

The composite medium infinite line source model (CMILS) was recently developed to describe the heat transfer of borehole ground heat exchanges. But this model is very complicated and time-consuming to calculate the solutions, which limit its practical applications. This paper presents a method to simplify the CMILS model and develops short time-step response g-functions using the simplified CMILS model. The advantage of the new short time-step response g-functions is that they are simple in calculation with comparable accuracy compared with CMILS model. Simulation studies show that g-functions calculated by simplified CMILS model match nicely with the experimental data. Detailed comparisons are also carried out between the simplified CMILS model and other numerical or analytical models through simulation.

ADC-Based Embedded Real-Time Simulator of a Power Converter Implemented in a Low-Cost FPGA: Application to a Fault-Tolerant Control of a Grid-Connected Voltage-Source Rectifier

This paper deals with embedded real-time (RT) simulators applied in power electronic applications and implemented in low-cost field-programmable gate arrays. Indeed, such simulators' intellectual properties (IPs) are not only intended for hardware-in-the-loop (HIL) testing but also can be advantageously embedded within digital controllers to ensure functions such as observation, estimation, diagnostic, or health monitoring. Conversely, to the HIL case, the main challenge when designing such simulators' IPs is to cope with their complexity having in mind that, in the case of embedded systems, the available hardware resources are limited due to the cost. Furthermore, this challenge is strengthened by the need of very short simulation time steps that is typically the case when simulating power converters. By this way, this paper presents the design of an embedded RT simulator of a three-phase grid-connected voltage-source rectifier, based on the associated discrete circuit modeling approach. This IP is associated with the one of a three-phase $RL$ filter, and both are implemented within the rectifier controller to estimate the grid currents. The latter is injected in the controller when a fault is detected in the current sensors. The ability of this estimator to guarantee the service continuity in case of faults has been validated through HIL tests and experiments.

Error correction in short time steps during the application of quantum gates

We propose a modification of the standard quantum error-correction method to enable the correction of errors that occur due to the interaction with a noisy environment during quantum gates without modifying the codification used for memory qubits. Using a perturbation treatment of the noise that allows us to separate it from the ideal evolution of the quantum gate, we demonstrate that in certain cases it is necessary to divide the logical operation in short time steps intercalated by correction procedures. A prescription of how these gates can be constructed is provided, as well as a proof that, even for the cases when the division of the quantum gate in short time steps is not necessary, this method may be advantageous for reducing the total duration of the computation.

A New Class of Quality Controls for Micrometeorological Data in Complex Tropical Environments

AbstractQuality control is a particularly demanding problem for micrometeorological studies in complex environments. With the transition to electronic sensing and storage of climate data in high temporal resolution, traditional approaches of homogenization are insufficient for addressing the small-scale variability and spatial heterogeneity of the data. This problem can be successfully addressed by introducing a new class of control procedures based on the physical and climatological relations between different climate variables. The new approach utilizes knowledge about the interdependency of air temperature, precipitation, radiation, relative air humidity, cloud cover, and visibility to develop empirical functions for determining the probability margins for the co-occurrence of specific conditions in tropical mountains and deserts. It can also be applied to other geographic settings by adjusting the parameters derived from the data itself. All procedures are integrated into a processing chain with feedback loops and combined with conventional logical and statistical checks, which enables it to detect small errors that normally pass unnoticed. The algorithms are also adapted to incorporate the short time steps of the original data to retain the potential for detailed process analyses.

Real-Time TD-DFT with Classical Ion Dynamics: Methodology and Applications.

We present a method for real-time propagation of electronic wave functions, within time-dependent density functional theory (RT-TDDFT), coupled to ionic motion through mean-field classical dynamics. The goal of our method is to treat large systems and complex processes, in particular photocatalytic reactions and electron transfer events on surfaces and thin films. Due to the complexity of these processes, computational approaches are needed to provide insight into the underlying physical mechanisms and are therefore crucial for the rational design of new materials. Because of the short time step required for electron propagation (of order ∼10 attoseconds), these simulations are computationally very demanding. Our methodology is based on numerical atomic-orbital-basis sets for computational efficiency. In the computational package, to which we refer as TDAP-2.0 (Time-evolving Deterministic Atom Propagator), we have implemented a number of important features and analysis tools for more accurate and efficient treatment of large, complex systems and time scales that reach into a fraction of a picosecond. We showcase the capabilities of our method using four different examples: (i) photodissociation into radicals of opposite spin, (ii) hydrogen adsorption on aluminum surfaces, (iii) optical absorption of spin-polarized organic molecule containing a metal ion, and (iv) electron transfer in a prototypical dye-sensitized solar cell.

Efficient photoheating algorithms in time-dependent photoionization simulations

We present an extension to the time-dependent photo-ionization code C$^2$-Ray to calculate photo-heating in an efficient and accurate way. In C$^2$-Ray, the thermal calculation demands relatively small time-steps for accurate results. We describe two novel methods to reduce the computational cost associated with small time-steps, namely, an adaptive time-step algorithm and an asynchronous evolution approach. The adaptive time-step algorithm determines an optimal time-step for the next computational step. It uses a fast ray-tracing scheme to quickly locate the relevant cells for this determination and only use these cells for the calculation of the time-step. Asynchronous evolution allows different cells to evolve with different time-steps. The asynchronized clocks of the cells are synchronized at the times where outputs are produced. By only evolving cells which may require short time-steps with these short time-steps instead of imposing them to the whole grid, the computational cost of the calculation can be substantially reduced. We show that our methods work well for several cosmologically relevant test problems and validate our results by comparing to the results of another time-dependent photo-ionization code.