Reduce Simulation Time Research Articles

Learning soft tissue deformation from incremental simulations.

Surgical planning for orthognathic procedures demands swift and accurate biomechanical modeling of facial soft tissues. Efficient simulations are vital in the clinical pipeline, as surgeons may iterate through multiple plans. Biomechanical simulations typically use the finite element method (FEM). Prior works divide FEM simulations into increments to enhance convergence and accuracy. However, this practice elongates simulation time, thereby impeding clinical integration. To accelerate simulations, deep learning (DL) models have been explored. Yet, previous efforts either perform simulations in a single step or neglect the temporal aspects in incrementalsimulations. This study investigates the use of spatiotemporal incremental modeling for biomechanics simulations of facial soft tissue. We implement the method using a graph neural network. Our method synergizes spatial features with temporal aggregation using DL networks trained on incremental FEM simulations from 17 subjects that underwent orthognathicsurgery. Our proposed spatiotemporal incremental method achieved a mean accuracy of 0.37 mm with a mean computation time of 1.52 s. In comparison, a spatial-only incremental method yielded a mean accuracy of 0.44 mm and a mean computation time of 1.60 s, while a spatial-only single-step method yielded a mean accuracy of 0.41 mm and a mean computation time of 0.05 s. Statistical analysis demonstrated that the spatiotemporal incremental method reduced mean errors compared to the spatial-only incremental method, emphasizing the importance of incorporating temporal information in incremental simulations. Overall, we successfully implemented spatiotemporal incremental learning tailored to simulate soft tissue deformation while substantially reducing simulation time compared toFEM.

Effect of hollow fiber membrane packing on the performance of modules formed with fiber tows

ABSTRACT Membrane processes are being considered for carbon dioxide capture from concentrated point sources. The processes often use hollow fiber membranes. Modules are formed by gathering fibers together in a bundle. The fibers may be supplied individually or in small groups (i.e. tows) for module fabrication. The use of tows can introduce nonuniform fiber packing due to the size and spacing of the tows. The potential for flow maldistribution and its detrimental effect on module performance is evaluated by solving the governing conservation equations. For the first time, the performance of a module formed from fiber tows is evaluated. Two performance metrics are reported: 1) recovery and 2) required area as a function of carbon dioxide removal. The effects of tow size and tow spacing are evaluated. The results indicate performance is better for smaller tows. Furthermore, lower packings, both intra- and inter-tow, are preferred. The concept of an equivalent planar bundle (EPB) for fiber tow modules is introduced to potentially reduce simulation time and costs. The simple procedure for creating the EPB is validated by comparing the performance metrics calculated using the EPB to the results obtained from full simulations.

Inverse modeling of electromagnetic emissions using grey wolf optimization

The paper proposes an inverse modeling approach for evaluating radiated electromagnetic compatibility (EMC) in electronic components and circuits. To imitate the electromagnetic behavior of real devices, the suggested methodology generates an equivalent model using elementary dipoles. The Grey Wolf Optimization (GWO) algorithm solves an inverse problem to identify dipole parameters such as locations, intensities, and orientations. This technique improves model accuracy and robustness through a two-phase exploration and exploitation process that allows for effective parameter tuning while reducing simulation time and computational resources. Recent research in near-field measurement techniques illustrates the importance of reliable predictive methodologies in EMC evaluation. This method provides significant information on the impacts of power systems on surrounding electronic circuits, making it a useful tool for EMC testing. It also promotes the development of immunity models for high-frequency applications. Overall, this methodology simplifies the examination procedure, resulting in higher design efficiency for a wide range of electronic systems.

Physics embedded neural network: Novel data-free approach towards scientific computing and applications in transfer learning

This paper introduces a novel approach for solving partial differential equations using neural networks for scientific computing applications. The proposed approach is referred to as physics embedded neural network (or PENN) due to its unique modified architecture designed to contain the partial differential equation information within the neural network, which is built upon a feed-forward neural network (NN) with fully connected layers. The key aspect of PENN is the numerical embedding of a differential equation associated with physical problem in the penultimate layer of the neural network. Here we propose that through such integration of PDE to the neural network’s penultimate layer, we can produce a fast numerical solution of the PDE, and with time performance comparable with Finite Element Method (FEM). Due to direct solution of the PDE, the NN solution occurs without training and testing phases which are normally applied when using NN in a data-based training. To demonstrate the effectiveness of the proposed architecture, we investigate variety of cases focused around second order in-homogeneous PDE in 2 dimensional (2D) problems. Additionally, we demonstrate the effectiveness of our approach by applying it to solve electromagnetic problem to illustrate its engineering applications. In this study, we also conducted a comparison of solution time and error achieved using our proposed network with a classical finite element method (FEM) solver. The convergence was found exponential with number of epochs proving an error significantly lower error compared to FEM and reported in other NN based algorithms such as Physics Informed Neural Networks. Furthermore, we explored the application of PENN in transfer learning. Our findings showed that by using transfer learning, up to 5 times additional reduction in simulation time is possible as compared to a direct solution through PENN. Overall, the study contributes to the development of efficient and accurate methods for solving PDEs through neural network optimization and provides important insights into the potential benefits of incorporating transfer learning techniques in numerical modeling of physical phenomenology.

Optimized Architecture for Efficient OFDMA Network Design

This study presents a novel approach to enhancing the design and performance of OFDMA (Orthogonal Frequency Division Multiple Access) networks, with a particular focus on WiMAX (Worldwide Interoperability for Microwave Access) for Best Effort (BE) services. The proposed method integrates a robust Markovian analytical model with four advanced scheduling algorithms: throughput fairness, resource fairness, opportunistic scheduling, and throttling. A sophisticated simulator was developed, incorporating an ON/OFF traffic generator, user-specific wireless channels, and a dynamic central scheduler to validate the model’s accuracy and evaluate its robustness by dynamically allocating radio resources per frame. The validation study showed that the proposed model reduced simulation time by over 90%, completing analytical calculations in just 15 min, compared to nearly 2 days for simulations using conventional scheduling algorithms. Performance metrics such as the average number of active users and resource utilization closely matched those from the validation study, confirming the model’s accuracy. In the robustness study, the model consistently performed well across diverse traffic distributions (exponential and Pareto) and channel conditions. The proposed architecture increased network throughput by up to 25% and reduced latency under dynamic conditions, demonstrating its scalability, adaptability, and efficiency as a crucial solution for next-generation wireless communication systems.

A modified variational approach to noisy cell signaling.

Signaling in cells is full of noise and, hence, described with stochastic biochemical models. Thus, an efficient computation algorithm for these fluctuating reactions is much needed. Apart from the very popular Monte Carlo simulation, methods based on probability distributions are frequently desired due to their analytical tractability and possible numerical advantages in diverse circumstances, among which the variational approach is the most notable. In this paper, new basis functions are proposed to better depict possibly complex distribution profiles, and an extra regularization scheme is supplied to the variational equation to remove occasional degeneracy-induced singularities during the evolution. The new extension is applied to four typical biochemical reaction models and restores the Gillespie results accurately but with greatly reduced simulation time. This modified variational approach is expected to work in a wide range of cell signaling networks.

A parallel compositional reservoir simulator for large-scale CO2 geological storage modeling and assessment

Storing CO2 in deep aquifers and depleted gas reservoirs is an effective way to achieve carbon neutrality. However, the numerical simulation of CO2 storage in these formations is challenging due to the complexity of gases-brine systems. The number of gas species included in the gases-brine fluid models of existing simulators cannot meet the rapidly evolving CO2 sequestration scenarios. To address this intricate issue, we developed a three-dimensional fully implicit parallel CO2 geological storage simulator (PRSI-CGCS) on distributed-memory computers based on our in-house parallel platform. This simulator uses a compositional fluid model with a diverse range of gas species, including CO2, C1 ~ C3, N2, H2S, as well as newly added gases H2 and O2, which may be encountered in geological CO2 storages. Besides, we provide more suitable scaling factors for different gases in the stability analysis bypassing (SAB) method to accelerate the gases-brine phase equilibrium calculations. PRSI-CGCS does not incorporate energy conservation equations, and salt precipitation or dissolution is also not considered. Numerical experiments show that our simulator is scalable, robust and validated to simulate large-scale CO2 storage problems with hundreds of millions of grid blocks on a parallel supercomputer cluster. Besides, after our modification on scaling factors, the SAB method can reduce the number of stability analyses by 61.39 % to 88.71 %, thereby reducing simulation time. Furthermore, case studies indicate that injecting O2 and H2 along with CO2 reduces the stability or capacity of CO2 storage and increases the pressure required for injection. However, this impact is not significant when the impurity content is less than 10 %.

A multiscale model for efficiently simulating laser powder bed fusion process with detailed microstructure and mechanical performance results

Numerical simulation is regarded as an important method for studying the mechanisms of additive manufacturing (AM), especially in building a multiscale simulation model. However, the conversion of physical phenomena and parameters across scales is complex, and the number of simulation elements often changes extremely, leading to an inherent conflict between simulation accuracy and efficiency. Therefore, this work introduces a model that balances the need for detailed grain morphology and overall simulation efficiency, to investigate the relationship between process parameters, microstructure, and mechanical performance during Inconel 718 laser powder bed fusion (L-PBF) process. The cellular automata - finite element method (CA-FEM) was used to simulate the melt pool forming and predict the microstructure evolution. Based on the CA result, the tensile process was simulated through crystal plasticity-finite element method (CP-FEM). Specially, the CA-FEM model was simplified and sliced layer-by-layer to reduce simulation time and data storage, supporting parallel computation. The prediction time for the microstructure growth of millions of elements was less than 1.5 h. The CP-FEM model was simplified by reasonably reducing elements in the representative volume element (RVE) model, improving the simulation efficiency by 73 %. The simulation results were validated through EBSD observation and tensile tests, showing good agreement with experimental results, with the final simulation error for mechanical performance not exceeding 10 %. The effects of process parameters on microstructure and mechanical performance were comprehensively discussed. This model supports the optimization of L-PBF process parameters for Ni-based alloys and provides a reference for improving the efficiency of multiscale simulations for other AM processes and materials.

Optimising building performance for a resilient Future: A Multi-Objective approach to Net Zero energy strategies

The escalating impacts of climate change on urban environments underscore the imperative for energy-efficient buildings. As the building sector constitutes approximately 40% of global energy consumption, the implementation of NZE designs is critical for emission reduction. This study utilised Building Performance Optimisation methodologies alongside a multi-stage optimisation framework to evaluate energy consumption, Life cycle cost and carbon emissions under various climate scenarios (RCP 2.6, 4.5, and 8.5) in three Algerian cities—Constantine (semi-arid), Algiers (Mediterranean), and Ghardaïa (arid).The results revealed that the integration of passive, active, and renewable energy strategies significantly curtailed energy consumption and CO2 emissions across different climatic contexts. Specifically, passive measures achieved reductions in energy use ranging from 39% in Ghardaïa to 15% in Constantine. Active systems, including high-efficiency HVAC technologies, resulted in energy savings of 59% in Ghardaïa, 52% in Algiers, and 47% in Constantine. Furthermore, renewable energy sources, with a focus on solar photovoltaics, contributed additional reductions: 44% in Algiers, 26% in Ghardaïa, and 20% in Constantine. The multi-stage optimisation approach also enhanced computational efficiency, significantly reducing simulation time and facilitating the rapid identification of optimal strategies.These findings highlight the efficacy of integrating a range of energy strategies to achieve NZE. Nevertheless, while these systems demonstrate robust performance under current conditions, their effectiveness diminishes under future climate scenarios, underscoring the necessity for adaptive and resilient design approaches. Ongoing optimisation and innovation will be essential to maintaining the efficacy of NZE strategies in the face of extreme future climate conditions.

Numerical investigation on a precast bridge using GPC and BFRP reinforcements subjected to cross-fault rupture and fling step excitation

This study investigates the seismic performances of a precast bridge made of geopolymer concrete (GPC) with fibre-reinforced polymer (FRP) reinforcements subjected to cross-fault ground motions. A numerical model was developed and verified against experimental results from a previous study and then used to evaluate the bridge's performances under earthquake excitations. The study found that a simplified model was able to reliably capture the failure pattern and displacement response of the bridge, reducing simulation time significantly. Additionally, the numerical results indicated the combination of torsional and flexural cracks was the primarily damage mode of the columns, which was not observed in the experimental test. This study also revealed that while the performances of the bridge using ordinary Portland cement (OPC) and GPC were similar under low ground excitations, GPC columns were more susceptible to brittle failure under higher ground excitations due to their brittleness. The use of FRP reinforcements led to similar displacement response as steel reinforcements under low ground displacement excitation, although severe flexural and shear damages on the column of Bent 2 were observed due to the lower elastic modulus and shear resistance of Basalt FRP material than steel. To address the disadvantages of brittle GPC and low-modulus of basalt FRP reinforcements, it is suggested to reinforce GPC with fibres and/or increase stirrup ratios if green GPC and corrosion-resistant basalt FRP reinforcements are used to construct bridges for seismic resistance.

A Comprehensive Analog–Mixed Signal (AMS) Simulations Environment

The analog–mixed signal simulation environment, used for verifying non-volatile memory macrocells, is presented. It has been adopted over the last decade, providing excellent results in verification coverage, efficiency, and flexibility. This methodology ensures a smooth and effective transition from full transistor/fully analog simulations to fully digital simulations while maintaining most of the environment’s features. This allows verification designers to exchange data, stimuli, and results, thereby enhancing debugging capabilities and reducing simulation time.

Computational Modeling Approach to Profile Hemodynamical Behavior in a Healthy Aorta.

Cardiovascular diseases (CVD) remain the leading cause of mortality among older adults. Early detection is critical as the prognosis for advanced-stage CVD is often poor. Consequently, non-invasive diagnostic tools that can assess hemodynamic function, particularly of the aorta, are essential. Computational fluid dynamics (CFD) has emerged as a promising method for simulating cardiovascular dynamics efficiently and cost-effectively, using increasingly accessible computational resources. This study developed a CFD model to assess the aorta geometry using tetrahedral and polyhedral meshes. A healthy aorta was modeled with mesh sizes ranging from 0.2 to 1 mm. Key hemodynamic parameters, including blood pressure waveform, pressure difference, wall shear stress (WSS), and associated wall parameters like relative residence time (RRT), oscillatory shear index (OSI), and endothelial cell activation potential (ECAP) were evaluated. The performance of the CFD simulations, focusing on accuracy and processing time, was assessed to determine clinical viability. The CFD model demonstrated clinically acceptable results, achieving over 95% accuracy while reducing simulation time by up to 54%. The entire simulation process, from image construction to the post-processing of results, was completed in under 120 min. Both mesh types (tetrahedral and polyhedral) provided reliable outputs for hemodynamic analysis. This study provides a novel demonstration of the impact of mesh type in obtaining accurate hemodynamic data, quickly and efficiently, using CFD simulations for non-invasive aortic assessments. The method is particularly beneficial for routine check-ups, offering improved diagnostics for populations with limited healthcare access or higher cardiovascular disease risk.

An approach simulating interacting solid, liquid, and gas domains for dynamic seal applications

AbstractIn seal applications a solid elastic body (the seal) ensures the separation of a liquid (e.g., hydraulic oil in one chamber) from a gas (e.g., air in another chamber). In the case of a dynamic seal, the rod is moving and transports a thin liquid film from the liquid chamber into the air chamber. The seal gap consists of a converging gap, a minimum distance between seal and rod and a diverging gap, where transported liquid detaches from the seal. Between the three states of matter (gas, liquid, gas) appear the following contact conditions: liquid‐to‐solid, gas‐to‐liquid, and gas‐to‐solid. A classical fluid‐structure‐interaction is technically possible with limited effort, but is not sufficient to distinguish between the liquid and the gas. A solution can make use of the fact, that the liquid has significant dimensions only in the liquid chamber and is pressurized only there. There is a thin liquid film on the rod in the air chamber, but it has dimensions clearly lower than the air chamber and has the same pressure as the air. Therefore a simulation is possible with the “variable viscosity approach”: Liquid and gas are modeled in one single fluid domain. Differences between liquid and gas are included by pressure‐dependent fluid parameters, especially viscosity and density. The resulting violation of the mass balance is very small as the low mass flow through the seal lip is low. The presented approach allows to apply a fluid‐structure simulation with special fluid properties to model a system with three states of matter. Advantages are a less complex model with less complex contact conditions and a reduced simulation time.

Two-level parallel load balancing strategy for accelerating DSMC simulations in near-continuum gases

The Direct Simulation Monte Carlo (DSMC) algorithm is widely employed for simulating rarefied gas flows and is increasingly applied in near-continuum regimes for research and engineering purposes. However, its computational demands, notably load imbalance and extended simulation time, hinder widespread adoption. Addressing these challenges, this paper introduces the Two-Level parallel load balancing strategy. This novel approach combines thread-level and multi-process parallelism to enhance load balancing and reduce simulation time. Key features include a thread-level load-decoupling strategy implemented via OpenMP and a multi-process load balancing mechanism employing distributed memory via MPI. Building upon our previous [Formula: see text] [L. Li, W. Ren and B. Zhang, J. Aeronaut. Astronaut. Aviat. Ser. A 46, 88 (2014)] approach, the load balancing mechanism utilizes Stop At Risk (SAR) criteria for repartitioning with METIS. Additionally, a specialized data transmission mechanism utilizing MPI nonblocking communication minimizes global communication between processes. Validation and evaluation are performed using four hypersonic flow cases around a cylinder and sphere, demonstrating significant improvements. Notably, the proposed strategy achieves [Formula: see text] enhancement over the [Formula: see text] strategy under 512 CPU cores compared to 16 CPU cores, and reduces between-process communication time with [Formula: see text]. These advancements contribute to enhancing the effectiveness of the DSMC algorithm in near-continuum aerodynamic simulations.

Optimization framework for daylight and thermal environment of retractable roof natatoriums based on generative adversarial network and genetic algorithm

This paper proposes a framework for multi-objective optimization of indoor daylighting and thermal comfort in natatoriums with retractable roofs, using genetic algorithms and building performance simulation. The goal is to balance daylight illumination and thermal comfort under different roof opening states. Efficiency of computational fluid dynamics simulation is improved by a multi-objective optimization framework based on non-dominated sorting genetic algorithms, integrating a generative adversarial network to learn the environmental map. The study analyses the impact of different roof opening ratios on environmental objectives and establishes regression equations to support optimization and accurate decision-making. In the optimal opening state, compared to a fully closed roof, the daylight factor and natural airflow velocity increase by up to 3.9 and 5.3 times, respectively, while the universal thermal climate index decreases by 1.0 °C. The introduction of a generative adversarial network proxy model significantly improves computational efficiency, accelerating natural airflow velocity calculation by 70–100 times and reducing simulation time by 98.6 %. This study expands predictive models from the urban scale to the building scale, enhancing simulation efficiency and promoting the application of deep learning models and genetic algorithms in climate-responsive building environment assessment and prediction.

Fast uncertainty assessment of in-service thrust control for turbofan engines: An equivalent model using Taylor expansion

An equivalent model using Taylor expansion (TEEM) is proposed for a fleet of engines regulated by the industrial baseline controller, aiming at the fast assessment of in-service thrust control under gas path and measurement uncertainties in advance. TEEM is fulfilled initially by the equivalent transformation of measurement uncertainties into engine set-point distribution, followed by a first-order Taylor expansion on the steady-state aero-thermal engine model along the average degradation curve of engine fleets. Simulations are conducted at take-off states on a validated aero-thermal turbofan engine model with publicly available uncertainty statistics on a desktop computer. Results show that the equivalent transformation is successful for both new and degraded engine fleets. Moreover, TEEM can estimate the mean and standard deviation values of key engine control parameters including thrust with the maximum errors of 0.04 % and 3.85 % for new engine fleets, 0.04 % and 6.25 % for degraded engine fleets, respectively, compared to the classic sample-based Monte-Carlo simulations (MCS). Computational time for TEEM and MCS for the tested life cycle are 3,018,564s and 137.52s accordingly, which means 99.995 % simulation time reduction is achieved by TEEM. Hence, the accuracy and efficiency of the proposed model for uncertainty assessment of thrust control of turbofan engines are confirmed.

Conjointly active and passive modelings with deep neural networks as fully automated optimizations for upper-mid band 6G communications

Today wireless systems include the fifth and sixth generations (5G and 6G) technologies and are growing day by day that result in exponentially increasing data traffic. For providing a reliable and high performance radio frequency (RF) designs especially for 6G networks, amplifiers and antenna as active and passive components play important roles. In the 5G/6G communication systems, the propagation loss is considerably large and its compensation requires high output power generated from the amplifiers for guaranteeing the satisfied quality of transmitted signal. From another point of view, the installed antennas must be able to optimally manage the radiated signals and handle/compensate nonlinear performances of the RF circuitry. Hence, advanced modeling and multi-objective optimization algorithms are required for designing and optimizing high performance amplifiers and antennas in terms of output power, gain, efficiency, linearity, and bandwidth. Concurrently optimizing active and passive components is not straightforward and typically it requires additional efforts by the RF designers. To tackle this drawback, a two-step methodology is proposed: (1) configuring the initial structure of active and passive devices, and (2) sizing the configured devices. In this work, various methods are introduced for structuring the topology of circuits and then artificial intelligence, including machine learning and neural networks, is preferred among other surrogate modelling for sizing the designs. These neural networks are satisfied due to the accurate modeling responses and are able to provide an automated optimization process leads to employ multi-objective optimization methods. In this work, an automated optimization process for comprehensive design of high-performance amplifiers with antennas through bottom-up optimization (BUO) method and long short-term memory (LSTM)-based deep neural networks (DNNs) is proposed. At the output layer of DNNs, the multi-objective multi-verse optimizer (MOMVO) method is employed for optimizing various specifications of active device (i.e., amplifier), and passive device (i.e., antenna), concurrently. In the presented method, all the electromagnetic (EM) design rules are implemented which results in reducing simulation time in the harmonic balance simulation environment that also provides ready to fabricate layouts. The novelty consists of the all-inclusive style that (1) reduces the manual breaks, aka time-to-market, and (2) delivers ready-to-fabricate layouts of the device that exhibits global optimum performances, automatically. The validation of the proposed method is verified by designing and optimizing high power amplifier (HPA) with antenna in the frequency band from 9.0 GHz to 9.6 GHz, suitable for upper-mid band 6G communications.

An insight into the effect of different parameters for optimizing parallel reservoir simulation performance

Parallel simulation significantly reduces runtime in oil reservoir simulations, enabling higher-resolution analysis and a better understanding of reservoir behavior. This study comprehensively evaluates how simulation time, hardware configuration, and various physical parameters impact the efficiency, scalability, and performance metrics such as run time reduction (RTR) and number of optimal cores (NOC) in parallel simulations. This study introduced the reduced simulation time (RST) concept, an innovative approach that enhances parallel simulation efficiency, and dynamic load balance. In this approach, simulations were performed using only 5% of the total simulation time. The findings reveal that in 80% of the models, switching to RST mode has no effect on NOC but significantly reduces overall execution time in most cases. In complex models, this time reduction can be as high as 60% compared to serial mode. In the remaining 20%, the number of cores in the total simulation time (TST) mode may be higher than in the RST mode, but this difference can be disregarded due to limited hardware resources and no change in RTR.

Design of encoded graphene-gold metasurface-based circular ring and square sensors for brain tumor detection and optimization using XGBoost algorithm

This study introduces a circular ring and square metasurfaces-based sensor employing graphene and gold layers for enhanced brain tumor detection. The sensor architecture includes dual graphene circular metasurfaces and a gold square resonator layer on a silicon dioxide substrate. A comprehensive parametric investigation explores the influence of geometric parameters and graphene chemical potential on sensor performance. The sensor achieves a remarkable sensitivity of 769 GHzRIU−1, a high-quality factor of 6.514, a low detection limit of 0.182 RIU, and an FOM of 1.148RIU−1. Electric field intensity analysis identifies optimal transmission frequencies. By employing the XGBoost regressor, the analysis significantly reduces simulation time and resource consumption by at least 80 %. Simulation validation confirms that despite 80 % reduction in simulation time, high prediction accuracy remains achievable, with an impressive R2 score ranging from 0.9 to 1. The proposed sensor presents a promising non-invasive approach for early brain tumor diagnosis, with potential applications in biomedical imaging and other related fields.

A reduced model for particle calcination for use in DEM/CFD simulations

We treat the accurate simulation of the calcination reaction in particles, where the particles are large and, thus, the inner-particle processes must be resolved. Because these processes need to be described with coupled partial differential equations (PDEs) that must be solved numerically, the computation times for a single particle are too high for use in simulations that involve many particles. Simulations of this type arise when the Discrete Element Method (DEM) is combined with Computational Fluid Dynamics (CFD) to investigate industrial systems such as quicklime production in lime shaft kilns.We show that, based on proper orthogonal decomposition and Galerkin projection, reduced models can be derived for single particles that provide the same spatial and temporal resolution as the original PDE models at a considerably reduced computational cost. Replacing the finite volume particle models with the reduced models results in an overall reduction of the reactor simulation time by about 40% for the sample system treated here.