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At least 775 records · Page 43

PIV and Rotational Raman-Based Temperature Measurements for CFD Validation of a Perforated Plate Cooling Flow Part I

Film cooling is used in a wide variety of engineering applications for protection of surfaces from hotor combusting gases. The design of more efficient film cooling geometries/configurations could be facilitated by an ability to accurately model and predict the effectiveness of current designs using computational fluid dynamics (CFD) code predictions. Hence, a benchmark set of flow field property data were obtained to assess current CFD capabilities and develop better modeling approaches for these turbulent flow fields where accurate calculation of turbulent heat flux is important. Both Particle Image Velocimetry (PIV) and spontaneous rotational Raman scattering (SRS) spectroscopy were used to acquire high quality, spatially-resolved measurements of the mean and root mean square (rms) velocities as well as the mean and rms temperatures in a film cooling flow field. In addition to off-body flow field measurements, infrared thermography (IR) and thermocouple measurements on the plate surface enabled estimates of the film effectiveness. Raman spectra in air were obtained across a matrix of axial locations downstream from a 68.07 mm square nozzle blowing heated air over a range of temperatures (up to TR =2.7) and Mach numbers (up to Mach 0.9), across a 30.48 cm long plate equipped with three patches of 45 small (~1 mm) diameter cooling holes arranged in a staggered configuration. In addition, both streamwise 2-component PIV (along the plate centerline) and cross-stream 3-component Stereo PIV data at 14 axial stations were collected in the same flows. Only a subset of the data collected in the test program is included in this Part 1 report. The rest of the data will be published in a future report, Part 2, along with planned CFD predictions of the complex cooling film flow.The entire data set of Raman temperature data, PIV velocity data and IR camera data covering the Set Points 23 and 49 in the test matrix in Table 1 is available in an accompanying DVD (available online from www.sti.nasa.gov) for those interested in further analysis.

Mark P Wernet↗

Numerical Investigation and Optimization of a Flushwall Injector for Scramjet Applications at Hypervelocity Flow Conditions

An investigation utilizing Reynolds-averaged simulations (RAS) was performed in order to demonstrate the use of design and analysis of computer experiments (DACE) methods in Sandia’s DAKOTA software package for surrogate modeling and optimization. These methods were applied to a flow- path fueled with an interdigitated flushwall injector suitable for scramjet applications at hyper- velocity conditions and ascending along a constant dynamic pressure flight trajectory. The flight Mach number, duct height, spanwise width, and injection angle were the design variables selected to maximize two objective functions: the thrust potential and combustion efficiency. Because the RAS of this case are computationally expensive, surrogate models are used for optimization. To build a surrogate model a RAS database is created. The sequence of the design variables comprising the database were generated using a Latin hypercube sampling (LHS) method. A methodology was also developed to automatically build geometries and generate structured grids for each design point. The ensuing RAS analysis generated the simulation database from which the two objective functions were computed using a one-dimensionalization (1D) of the three-dimensional simulation data. The data were fitted using four surrogate models: an artificial neural network (ANN), a cubic polynomial, a quadratic polynomial, and a Kriging model. Variance-based decomposition showed that both objective functions were primarily driven by changes in the duct height. Multiobjective design optimization was performed for all four surrogate models via a genetic algorithm method. Optimal solutions were obtained at the upper and lower bounds of the flight Mach number range. The Kriging model predicted an optimal solution set that exhibited high values for both objective functions. Additionally, three challenge points were selected to assess the designs on the Pareto fronts. Further sampling among the designs of the Pareto fronts may be required to lower the surrogate model errors and perform more accurate surrogate-model-based optimization.

Shenoy, Rajiv R.↗

Large eddy simulation of particle dispersion analysis in a pressurized reactive fluid–particle system

Pressurized oxy-combustion (POC) is a promising candidate to reduce carbon emissions in power generation. Designing an effective burner plays a vital role in developing new combustion technologies. Because of high pressure, the volumetric fraction of particles in a pressurized oxy-combustor could be higher than that in the conventional combustor, consequently, the particle dynamics in the pressurized vessel need to be evaluated accordingly. Specifically, the present computational work analyzes the pattern of the particle dispersion by extracting the particle mass flow rate and the particle size distribution in the pressurized combustor. A large eddy simulation (LES) with the environment pressure 15-bar and 100 kWth thermal input of fuel particle has been performed. The particle mass flow rates sampled in several cross-section planes strongly fluctuate, indicating the impacts of the flame as well as the gas-phase flow on the particle movement. Animations of the particle-gas flow show that the flow recirculation plays a major role in producing the pulsing phenomenon of the particle mass flow rate.

Li, Lei↗

CRN Modeling of Ammonia RQL Combustion using a Partially-Stirred Reactor Approach

Ammonia is a promising alternative to hydrogen with high energy density and favorable storage and transport characteristics. However low flammability and a propensity for high nitrogen oxide (NOx) emissions make direct utilization challenging. Recently, two-stage rich-quench-lean (RQL) combustion strategies have shown promise in achieving low NOx emissions with ammonia. In this approach, the rich stage serves to oxidize a portion of the fuel, while thermally decomposing as much of the remaining ammonia as possible, generating hydrogen. In the second (lean) stage, air is rapidly introduced, burning out the hydrogen and residual ammonia. Two-stage RQL combustion of ammonia has been investigated in the open literature both experimentally and numerically. In general, idealized chemical reactor network (CRN) models predict NOx concentrations below that of 2D/3D computational fluid dynamics models and experiments. The primary drivers of these discrepancies may be largely attributed to finite rate mixing non-adiabatic operation. The typical CRN model is comprised of a perfectly-stirred-reactor (PSR), followed by a plug-flow-reactor (PFR), meant to represent the flame, and post-flame zones, respectively. In the two-stage RQL approach two PSR-PFR networks are arranged sequentially, corresponding to the rich and lean stages, with secondary air injection in between. In the authors’ past work, this arrangement has demonstrated the significant sensitivity of exit NOx to the rich stage equivalence ratio, while the amount of secondary air injection was shown to be less critical. In this paper, the CRN model is extended to (1) include the impacts of heat loss and (2) utilize a partially-stirred-reactor (PaSR) approach to study the impacts of mixing on emissions performance. Varying amounts of heat loss are applied to the rich relaxation zone to understand emissions performance and changes to optimization of equivalence ratio and residence time. Premixed and non-premixed configurations are considered in the rich stage PaSR, with varying degrees of mixing intensity to study the interaction between mixing, transport, and kinetic timescales. Critically, the impact of mixing between hot products and secondary air injection is studied to understand practical injector needs. Results show unburnt ammonia leaving the rich stage as a primary contributor to NOx emissions – driven both by increased heat loss and reduced mixing rates. Furthermore, heat losses have shown to create conditions which are conducive to increased N2O formation in the lean stage. The results of this study will be considered in the context of developing optimized two-stage RQL combustors for ammonia..

advanced gas turbines↗

Mixing and NOx Emission Calculations of Confined Reacting Jet Flows in Cylindrical and Annular Ducts

Rapid mixing of cold lateral jets with hot cross-stream flows in confined configurations is of practical interest in gas turbine combustors as it strongly affects combustor exit temperature quality, and gaseous emissions in for example rich-lean combustion. It is therefore important to further improve our fundamental understanding of the important processes of dilution jet mixing especially when the injected jet mass flow rate exceeds that of the cross-stream. The results reported in this report describe some of the main flow characteristics which develop in the mixing process in a cylindrical duct. A three-dimensional computational fluid dynamics (CFD) code has been used to predict the mixing flow field characteristics and NOx emission in a quench section of a rich-burn/quick-mix/lean-burn (RQL) combustor. Sixty configurations have been analyzed in both circular and annular geometries in a fully reacting environment simulating the operating condition of an actual RQL gas turbine combustion liner. The evaluation matrix was constructed by varying the number of orifices per row and orifice shape. Other parameters such as J (momentum-flux ratio), MR (mass flowrate ratio), DR (density ratio), and mixer sector orifice ACd (effective orifice area) were maintained constant throughout the entire study. The results indicate that the mixing flow field can be correlated with the NOx production if they are referenced with the stoichiometric equivalence ratio value and not the equilibrium value. The mixing flowfields in both circular and annular mixers are different. The penetration of equal jets in both annular and circular geometries is vastly different which significantly affects the performance of the mixing section. In the computational results with the circular mixer, most of the NOx formation occurred behind the orifice starting at the orifice wake region. General trends have been observed in the NOx production as the number of orifices is changed and this appears to be common for all hole configurations and mixer types (circular or annular). The performance of any orifice shape (in producing minimum NOx) appears to be acceptable if the number of orifices can be freely varied in order to attain the optimum jet penetration.

Oechsle, Victor L.↗

A theoretical evaluation of rigid baffles in suppression of combustion instability

An analytical technique for the prediction of the effects of rigid baffles on the stability of liquid propellant combustors is presented. This analysis employs a three dimensional combustor model characterized by a concentrated combustion source at the chamber injector and a constant Mach number nozzle. An eigenfunction-matching method is used to solve the linearized partial differential equations describing the unsteady flow field. Boundary layer corrections to this unsteady flow are used in a mechanical energy dissipation model to evaluate viscous and turbulence effects within the flow. An integral stability relationship is then employed to predict the decay rate of the oscillations. Results of this analysis agree qualitatively with experimental observations and show that sufficient dissipation exists to indicate that the proper mechanism of baffle damping is a fluid dynamic loss. The response of the dissipation model to varying baffle blade length, mean flow Mach number and oscillation amplitude is examined.

Combustion instability↗

Chug and Dynamics of the RS-84 Subscale Preburner

The development of the RS-84 engine began in 2002 as part of the Space Launch Initiative. It was intended to be a reusable liquid oxygen/RP-1 booster engine of approximately 1 Mlbf thrust. Part of the test campaign consisted of testing subscale components to study key technologies such as oxygenrich, liquid oxygen/RP-1 combustion. In late 2003, the subscale preburner completed 4 hot-fire tests at Stennis Space Center with various hardware configurations and operating conditions, but before all planned tests could be completed the RS-84 engine development program was canceled in 2004. Recently, there has been a renewed interest in the development of an oxygen-rich, liquid oxygen/RP-1 combustion engine. Aerojet Rocketdyne and NASA completed testing of the subscale preburner in 2014 at Marshall Space Flight Center in an effort to better understand the chug encountered during the 2003 testing and to collect performance information over a wider range of operating conditions. The 2003 and 2014 data sets included extreme chug oscillations that reached nearly 200% of the chamber pressure and were reduced to well below 10% of the chamber pressure by incorporating a fuel orifice upstream of the fuel manifold. Depending on the hardware configuration and operating condition, a wide range of chug oscillation amplitudes were encountered. The dynamics for both test series were characterized and the data were used in the development of a chug model.

Casiano, M. J↗

Learning reference governor for cycle-to-cycle combustion control with misfire avoidance in spark-ignition engines at high exhaust gas recirculation–diluted conditions

Cycle-to-cycle feedback control is employed to achieve optimal combustion phasing while maintaining high levels of exhaust gas recirculation by adjusting the spark advance and the exhaust gas recirculation valve position. The control development is based on a control-oriented model that captures the effects of throttle position, exhaust gas recirculation valve position, and spark timing on the combustion phasing. Under the assumption that in-cylinder pressure information is available, an adaptive extended Kalman filter approach is used to estimate the exhaust gas recirculation rate into the intake manifold based on combustion phasing measurements. The estimation algorithm is adaptive since the cycle-to-cycle combustion variability (output covariance) is not known a priori and changes with operating conditions. A linear quadratic regulator controller is designed to maintain optimal combustion phasing while maximizing exhaust gas recirculation levels during load transients coming from throttle tip-in and tip-out commands from the driver. During throttle tip-outs, however, a combination of a high exhaust gas recirculation rate and an overly advanced spark, product of the dynamic response of the system, generates a sequence of misfire events. In this work, an explicit reference governor is used as an add-on scheme to the closed-loop system in order to avoid the violation of the misfire limit. The reference governor is enhanced with model-free learning which enables it to avoid misfires after a learning phase. Experimental results are reported which illustrate the potential of the proposed control strategy for achieving an optimal combustion process during highly diluted conditions for improving fuel efficiency.

42 ENGINEERING↗

Development and evaluation of a skeletal mechanism for EHN additized gasoline mixtures in large Eddy simulations of HCCI combustion

Advanced Low Temperature Combustion modes, such as the Sandia proposed Additive-Mixing Fuel Injection (AMFI), can unlock significant potential to boost fuel conversion efficiency and ultimately improve the energy conversion of internal combustion engines. This is a novel improved combustion process that is enabled by supplying small (<5%) variable amounts of autoignition improver to the fuel to enhance the engine operation and control. Common, diesel-fuel ignition-quality enhancing additive, 2-ethylexyl nitrate (EHN), is doped into gasoline to enable Sandia LTGC + AMFI combustion. This manuscript focuses on the development of a reduced sub-mechanism for EHN chemical kinetics at engine relevant conditions that is implemented into a skeletal mechanism for chemical kinetic studies of gasoline surrogate fuels. The mechanism validation utilized zero-dimensional numerical simulations and comparison to shock tube ignition-delay data of pure and EHN-doped n-heptane. Additional validation is presented with Homogeneous Charge Compression-Ignition (HCCI) engine data of pure and EHN-doped research-grade E10 gasoline. Then, the mechanism was deployed in a 3-D computational fluid dynamics (CFD) using Large Eddy Simulations (LES) to model the HCCI engine experiments of 0.4% vol EHN additized E10 gasoline at several equivalence ratios. Simulations showed a very good performance of the mechanism, and the model accurately reproduced (a) the ignition point, (b) combustion phasing, (c) combustion duration, and (d) the peak of the heat release rates of the engine experiments. The results show that EHN promotes Low-Temperature Heat Release, ultimately driving the gasoline to autoignite at thermodynamic conditions where the fuel would not otherwise ignite. Overall, this work demonstrates a viable reduced chemical-kinetic mechanism for EHN and shows that it can be combined with a skeletal gasoline mechanism for CFD-LES analysis of well-mixed LTGC that matches well with experimental results. The CFD-LES analysis also shows the spatial distribution of EHN-fuel interactions that control the autoignition throughout the combustion chamber.

Guleria, Gaurav↗

Comparison of a Full-Scale and a 1:10 Scale Low-Speed Two-Stroke Marine Engine Using Computational Fluid Dynamics

International marine shipping is a growing component of international trade; a vast majority of all the world’s goods are being transported on large ocean-going vessels. The International Maritime Organization (IMO) introduced the Energy Efficiency Design Index in 2013, a regulatory framework of associated metrics for reducing emissions of CO 2 per tonne-mile from shipping by approximately 10% each decade. Therefore, decarbonizing the maritime sector requires the development of new fuel sources. Because of the extremely large physical size of the internal combustion engines present in shipping vessels, experimental iterative development of the engine and fuel system is cost-prohibitive. Thus, the ability to perform combustion system development in a scaled platform that can be more easily operated and modeled computationally is of interest. To that end, scaling relationships are needed to translate the results from a smaller engine to a larger counterpart. Scaling studies to date have been restricted to low scaling ratios, four-stroke light-duty engines, and under-resolved computational fluid dynamic simulations that likely do not accurately capture the physics of scaling. In this work, computational models of a 1:10 scale and a full-scale two-stroke crosshead low-speed marine engine were created and validated against experiments obtained in a real 1:10 scale engine installed at Oak Ridge National Laboratory. Further, due to the large size of the full-scale engine, the model required large high-performance computing resources to be evaluated. The availability of high-performance computing resources at the Department of Energy’s Leadership Computing Facilities is an enabler of the current work. The results of the small- and large-scale engine simulations were compared to analyze the effectiveness of the appropriate scaling laws under these extreme scaling ratio conditions.

33 ADVANCED PROPULSION SYSTEMS↗

CFD modeling of non-catalytic, partial-oxidation engine reformer for flare mitigation

Flaring associated natural gas is commonly employed in the oil and gas industry to reduce methane (CH 4 ) emissions but generates carbon dioxide (CO 2 ) and harmful pollutants, significantly contributing to air pollution and posing risks to public health. To mitigate this impact, M2X Energy Inc. has developed a small-scale, modular gas-to-methanol system. This system features an engine reformer that performs fuel-rich partial oxidation of wellhead gas to produce syngas—a mixture of carbon monoxide (CO) and hydrogen (H 2 )—followed by a downstream reactor for methanol synthesis. This study focused on computational fluid dynamics (CFD) modeling of the engine reformer to simulate partial oxidation chemistry, predict the rich-burn operating limit, and assess syngas quality, ultimately aiding in design and operational optimization. The CFD model, developed within a Reynolds-Averaged Navier-Stokes (RANS) turbulence framework, incorporated sub-models for turbulent combustion, a chemical mechanism with polycyclic aromatic hydrocarbon (PAH) pathways, and soot emissions to accurately capture the fuel-rich, turbulent jet ignition and combustion processes. Model validation against experimental data showed good agreement across pre- and main-chamber pressures, apparent heat release rates, and exhaust gas concentrations of key species (H 2 , CO, CO 2 , CH 4 ) for varying intake equivalence ratios. Here, the model identified a rich-burn operating limit near a fuel-air equivalence ratio of 2.35, consistent with experimental observations. Furthermore, syngas quality analysis revealed that extending the rich-burn limit through engine reformer optimization could enhance syngas production, contributing to higher methanol synthesis efficiency.

Computational Fluid Dynamics↗

The black carbon cycle and its role in the Earth system

Black carbon (BC) is produced by incomplete combustion of biomass by wildfires and burning of fossil fuels. BC is environmentally persistent over centuries to millennia, sequestering carbon in marine and terrestrial environments. However, its production, storage and dynamics, and therefore its role in the broader carbon cycling during global change, are poorly understood. Here, in this Review, we discuss BC cycling across the land-to-ocean continuum. Wildfires are the main source of BC, producing 128 ± 84 teragrams per year. Negative climate–BC feedbacks could arise as wildfire increases with anthropogenic warming, producing more BC, which in turn will sequester carbon, but the magnitude of these effects are unknown. Most BC is stored in terrestrial systems with some transported to the ocean via rivers and the atmosphere. However, the oceanic BC budget is not balanced, with known BC removal fluxes exceeding BC inputs. We demonstrate these observed inconsistencies using a simple ocean box model, which highlights key areas of future research. Measurements of BC mineralization and export rates along the land-to-ocean continuum and quantification of previously unexplored sources of oceanic BC are needed to close the global BC budget.

aquatic↗

Characterization of Flex-Fuel Prechamber Enabled Mixing-Controlled Combustion With Gasoline/Ethanol Blends at High Load

This numerical study focuses on the characterization of prechamber-enabled mixing-controlled combustion (PC-MCC) at ~18 bar brake mean effective pressure (BMEP) and 2200 rpm with 10% by volume ethanol-gasoline blend (E10) and pure ethanol (E100). Computational fluid dynamic (CFD) simulations of a stock and prechamber retrofitted single-cylinder Caterpillar C9.3B are carried out using CONVERGE. Prechamber equivalence ratio at spark timing, prechamber spark timing advance, and main chamber injection strategy are assessed with respect to their impact on ignition assistance performance and emissions characteristics relative to a diesel baseline at the same boundary conditions. Simulation results indicate that PC-MCC is flex-fuel capable and operates well for both E10 and E100 at the operating conditions considered. The results demonstrate that the use of a pilot-main injection strategy enables spark timing in the prechamber to be advanced and thus reduces spark plug firing pressure while maintaining robust ignition assistance. Results also indicate that the rich prechamber operation is favored for improved ignition assistance capabilities. Furthermore, the findings of this work suggest that a heavy-duty vehicle using a PC-MCC engine can utilize any blend of gasoline and ethanol, up to including pure ethanol, with no major sacrifices in performance relative to the diesel engine.

33 ADVANCED PROPULSION SYSTEMS↗

In-cylinder spray evolution in a motored central-injection gasoline engine: Imaging and simulating the effects of flash-boiling and intake crossflow

Accurate predictions of fuel spray behavior and mixture formation in simulations of direct-injection spark-ignition (DISI) engines are fundamental to ensure proper description of all subsequent processes including ignition, combustion, and emissions. In this work, the spray evolution in a single-cylinder optical DISI engine was studied experimentally and numerically with the goal of enabling predictive computational fluid dynamics (CFD) modeling of in-cylinder sprays. The authors explored a wide range of operating conditions characterized by several fuel injection temperatures and engine speeds, using a well-characterized nine-component gasoline surrogate known as PACE-20. The effect of flash boiling and intake crossflow on the spray is discussed, with a focus on evaluating the ability of the spray models to capture highly transient spray behavior. In the experiments, the fuel temperature was varied between 20°C and 80°C, allowing for non-flash- to flash-boiling transition to emerge with enhanced flashing intensity at the highest temperatures. Spray collapse resulted in vapor-rich regions, owing to the locally lower inertia of the fluid. Varying the engine speed from 650 to 1950 rpm promoted increasingly more turbulent in-cylinder crossflow which interacted with the spray during the injection event and resulted in enhanced spray dispersion. The CFD model was able to capture the spray morphology transition at different fuel temperatures and engine speeds adequately. Further, it is shown that the spray breakup model could capture the transitional spray behavior induced by flash boiling atomization and intake flow via proper initialization of the spray cone angle and calibration of the spray models’ constants.

33 ADVANCED PROPULSION SYSTEMS↗

Heating effects on pyrogenic organic matter mass loss and temperature in a sand matrix in a lab setting from 2022

This dataset contains data associated with the preprint “A laboratory method for simulating the effects of subsequent fires on pyrogenic organic matter at different exposure depths in a sand matrix” (https://doi.org/10.1101/2024.07.30.605814), which has been accepted for publication in the International Journal of Wildland Fire. The dataset was generated to investigate the effects of subsequent fires on preexisting pyrogenic organic matter (PyOM) at different soil depths. Specifically, we designed a laboratory method to simulate soil heating from above, applying realistic heat flux profiles (High, Low, Control) derived from jack pine (Pinus banksiana Lamb.) log burns. Using a cone calorimeter, these profiles were applied to buried jack pine PyOM (produced at 350°C) in a sand matrix pyrocosm to examine PyOM mass loss at different depths (surface, 1 cm, 5 cm). Each treatment (e.g., High heat flux at 1 cm depth) was applied once to five replicates in a pyrocosm.The dataset includes mass loss fraction of PyOM and time-series temperature profiles (measured with type K thermocouples). Additionally, calibration datasets for high and low heat flux profiles are provided, including programmed heat flux profile data and three sets of calibration results. All datasets are in .csv format and were analyzed in R using code found at https://github.com/MengmengLuo/Reburning-pyrogenic-organic-matter-A-laboratory-method-for-dosing-dynamic-heat-fluxes-from-above. This dataset supports research on PyOM transformations during subsequent fires, and methodological advancements in simulating soil heating. It can be used to explore fire-induced PyOM alterations across different fire intensities and soil depths.

54 ENVIRONMENTAL SCIENCES↗

Developing an Eco-Cooperative Automated Control System (Eco-CAC)

The goal of the project was to develop a novel Eco-Cooperative Automated Control (Eco-CAC) system that integrates vehicle dynamics (VD) control with connected and automated vehicle (CAV) applications. In particular, the team developed a novel integrated control system that (1) routes vehicles in a fuel/energy-efficient manner for internal combustion engine vehicles (ICEVs), battery-only electric vehicles (BEVs), and hybrid electric vehicles (HEVs); (2) selects vehicle speeds based on anticipated traffic network evolution; (3) minimizes vehicle fuel/energy consumption near signalized intersections; and (4) intelligently modulates the longitudinal motion of vehicles within a cooperative platoon to minimize its fuel/energy consumption.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

An adaptive pseudo-spectral method for reaction diffusion problems

The spectral interpolation error was considered for both the Chebyshev pseudo-spectral and Galerkin approximations. A family of functionals I sub r (u), with the property that the maximum norm of the error is bounded by I sub r (u)/J sub r, where r is an integer and J is the degree of the polynomial approximation, was developed. These functionals are used in the adaptive procedure whereby the problem is dynamically transformed to minimize I sub r (u). The number of collocation points is then chosen to maintain a prescribed error bound. The method is illustrated by various examples from combustion problems in one and two dimensions.

Bayliss, A.↗

An adaptive pseudo-spectral method for reaction diffusion problems

The spectral interpolation error was considered for both the Chebyshev pseudo-spectral and Galerkin approximations. A family of functionals I sub r (u), with the property that the maximum norm of the error is bounded by I sub r (u)/J sub r, where r is an integer and J is the degree of the polynomial approximation, was developed. These functionals are used in the adaptive procedure whereby the problem is dynamically transformed to minimize I sub r (u). The number of collocation points is then chosen to maintain a prescribed error bound. The method is illustrated by various examples from combustion problems in one and two dimensions.

Bayliss, A.↗