Forward Mode Research Articles

Structural, Optical and Electrical Analysis of Pentacene Thin Film

The significant electrical characteristics of pentacene thin film was studied by fabricating silver-pentacene-aluminium sand witch device. This metal-semiconductor-metal (MSM) device can act as the diode . When investigating, it is found that the diode can act as an equivalent plate capacitor as reverse bias mode exclusive of current flow. In forward bias mode, studied diode as an equivalent circuit with a parallel circuit of resistance –capacitance. This paper describes analysis of capacitance by measuring I-V characteristics and impedance measurement. The free samples of pentacene are also analysed using field emission scanning electron microscope (FESEM) and X-ray diffraction micrographs (XRD) . The X-ray diffraction micrograph shows the configuration of pentacene in the (-1 0 2) plane as the strongest orientation .The particle size are analysed using FESEM. The optical characteristics are analysed using UV spectrometer. The spectra of absorption, reflection and refraction are studied well.

On the special role of NCX in astrocytes: Translating Na+-transients into intracellular Ca2+ signals

As a solute carrier electrogenic transporter, the sodium/calcium exchanger (NCX1-3/SLC8A1-A3) links the trans-plasmalemmal gradients of sodium and calcium ions (Na+, Ca2+) to the membrane potential of astrocytes. Classically, NCX is considered to serve the export of Ca2+ at the expense of the Na+ gradient, defined as a “forward mode” operation. Forward mode NCX activity contributes to Ca2+ extrusion and thus to the recovery from intracellular Ca2+ signals in astrocytes. The reversal potential of the NCX, owing to its transport stoichiometry of 3 Na+ to 1 Ca2+, is, however, close to the astrocytes’ membrane potential and hence even small elevations in the astrocytic Na+ concentration or minor depolarisations switch it into the “reverse mode” (Ca2+ import/Na+ export). Notably, transient Na+ elevations in the millimolar range are induced by uptake of glutamate or GABA into astrocytes and/or by the opening of Na+-permeable ion channels in response to neuronal activity. Activity-related Na+ transients result in NCX reversal, which mediates Ca2+ influx from the extracellular space, thereby generating astrocyte Ca2+ signalling independent from InsP3-mediated release from intracellular stores. Under pathological conditions, reverse NCX promotes cytosolic Ca2+ overload, while dampening Na+ elevations of astrocytes. This review provides an overview on our current knowledge about this fascinating transporter and its special functional role in astrocytes. We shall delineate that Na+-driven, reverse NCX-mediated astrocyte Ca2+ signals are involved neurone-glia interaction. Na+ transients, translated by the NCX into Ca2+ elevations, thereby emerge as a new signalling pathway in astrocytes.

Peak focusing based on stationary phase thickness gradient

This paper reports the development of a stationary phase thickness gradient gas chromatography (GC) column that enables analyte peak focusing and improves separation resolution. Theoretical analysis and simulation demonstrate focusing via a positive thickness gradient, i.e., the stationary phase thickness increases along the column. This effect was experimentally verified by coating a 5 m long capillary column with a film thickness varying from 34 nm at the column inlet to 241 nm at the column outlet. The column was analyzed in forward (thin to thick) and backward (thick to thin) modes and compared to a uniform thickness column with a thickness of 131 nm, using alkanes ranging from C5 to C16 and aromatics. Comparison of resolutions between forward mode and the uniform thickness column demonstrated an overall focusing rate (i.e., improvement in peak capacity) of 11.7% on alkanes and 28.2% on aromatics. The focusing effect was also demonstrated for isothermal room temperature separation of highly volatile compounds and temperature programmed separation with different ramping rates. In all cases, peak capacities from forward mode separations are higher than those from other modes, indicating the ability of a positive thickness gradient to focus analyte peaks. This thickness gradient technique can therefore be broadly applied to various stationary phases and column types as a general method for improving GC separation performance.

In-situ growth of metal-organic framework film on a polydopamine-modified flexible substrate for antibacterial and forward osmosis membranes

Metal-organic frameworks (MOFs), being a type of the most representative porous nanomaterials, have been regarded as a promising candidate to fabricate antibacterial separation membrane attributing to their high porosity, tunable pore size and chemical functionality. Comparing with the traditional blending techniques, depositing a continuous and coherent MOF crystal layer on top of the membrane can fully exploit the functionality of the materials. In this study, we constructed a continuous zeolite imidazole framework-8 (ZIF-8) crystal layer on the surface of flexible polysulfone (PS) membrane pre-modified by polydopamine (PDA) via a facile immersion strategy. The characterization results confirmed the formation of a continuous ZIF-8 coating layer, which significantly increases the roughness of composite membrane from 17.2 nm to 154.0 nm compared with PDA/PS substrates. The ZIF-8 layer deposited on the surface of the PDA/PS membrane reduced the contact angle value from 45.4° to 38.6° based on the properties of Janus membrane. As a result, the ZIF-8/PDA/PS composite membranes showed a high water flux of 9.6 L/m2·h and a low solute reverse flux of 3.8 g/m2·h using 1 M MgCl2 as draw solution and DI water as feed solution under forward osmosis mode. In addition, the composite membranes also exhibited a satisfactory antimicrobial performance against Escherichia coli (E. coli) with antibacterial efficiency almost 99%, which is much higher than PDA/PS membrane (64%). This work demonstrates a facile way to ZIF-8/PDA/PS composite membranes with good FO performance and excellent antibacterial capacities.

An introduction to algorithmic differentiation

AbstractAlgorithmic differentiation (AD), also known as automatic differentiation, is a technology for accurate and efficient evaluation of derivatives of a function given as a computer model. The evaluations of such models are essential building blocks in numerous scientific computing and data analysis applications, including optimization, parameter identification, sensitivity analysis, uncertainty quantification, nonlinear equation solving, and integration of differential equations. We provide an introduction to AD and present its basic ideas and techniques, some of its most important results, the implementation paradigms it relies on, the connection it has to other domains including machine learning and parallel computing, and a few of the major open problems in the area. Topics we discuss include: forward mode and reverse mode of AD, higher‐order derivatives, operator overloading and source transformation, sparsity exploitation, checkpointing, cross‐country mode, and differentiating iterative processes.This article is categorized under: Algorithmic Development > Scalable Statistical Methods Technologies > Data Preprocessing

GLAM Bio-Lith RT: A Tool for Remote Sensing Reflectance Simulation and Water Components Concentration Retrieval in Glacial Lakes

A new open--source software tool, called GLAM BioLith--RT (Glacier Lakes Assisted Melting Biological Lithological Radiative Transfer), has been developed for modeling of Radiative Transfer (RT) in water bodies containing suspended lithic particles , phytoplankton, dissolved salts, and colored dissolved organic matter. Although our objective is an application to glacial lakes of High Mountain Asia, the model has potential application for the study of seawater, organic-rich lakes, rivers, etc. The tool is built on a solid foundation of an existing published open-source code called WASI, which has been reviewed and augmented with new capabilities, notably the addition of a suspended lithic particle grain size parameterization. GLAM BioLith-RT operates in both a forward modeling and inverse modeling mode. The forward mode is specifically designed to compute the reflectance spectra of glacier lakes from inherent optical water properties. Conversely, in the inverse mode, measured spectral reflectance is employed with other inputs to derive best fitting water component properties (e.g., suspended particles concentration). The inverse modeling includes Bayesian Optimization of the output which is a significant advance over the existing software. We have tested the code for sensitivity to noise, and uncertainties in input parameters. The model succeeds in nearly reproducing the hyperspectral reflectance of some glacial lakes in Nepal as observed by the EO-1 Hyperion hyperspectral imager. The inverse modeling approach, when supported up by validated forward modeling, offers a means for remote sensing characterization of suspended sediment load in glacial lakes and rivers and hence, use of suspended sediment as a proxy for glacial activity; and many other potential applications in other thematic areas.

Analysis and Design of High-Efficiency Bidirectional GaN-Based CLLC Resonant Converter

A bidirectional CLLC resonant converter (CLLC-BRC) based on GaN transistors is analyzed and designed in this paper. Similar resonant topologies are listed and commented on, with the CLLC topology showing competitiveness in bidirectional energy transmission. The analysis of the aforementioned converter has been provided, including the reveal of resonant frequencies of the CLLC topology and an improved zero-voltage switching (ZVS) condition with operation principles of the reverse mode and relevant parasitic parameters taken into account. The design methodology of the aforementioned converter based on pulse frequency modulation (PFM) is further discussed in detail. A prototype with a rated power of 400 W and a maximal operating frequency that is larger than 0.5 MHz was built to verify the proposed design methodology. The highest conversion efficiency of the prototype was 97.02% in the forward mode, and it was 95.96% in the reverse mode.

Evaluation of the V SD ‐method for temperature estimation during power cycling of SiC‐MOSFETs

An accurate temperature estimation is a substantial necessity to evaluate the outcome of a power cycling test. For devices with a forward biased pn-junction in the main current path, there is a well-known and understood method using its forward voltage drop at a small sensing current. Since metal–oxide–semiconductor field-effect transistors (MOSFETs) do not provide a pn-junction in forward mode, this method cannot be applied directly. A similar method to estimate the junction temperature of a MOSFET is the VSD(T)-method, which uses the junction of the reverse body diode. While this method is gaining wide acceptance for junction temperature estimation during power cycling of silicon carbide MOSFETs, no comprehensive investigation on its accuracy, stability and susceptibility towards degradational shift has been performed so far. In this work, the results of an investigation on the VSD(T)-method with an evaluation of its precision and suitability for temperature estimation during power cycling tests of silicon carbide MOSFETs are presented.

Microfluidic Passive Flow Regulatory Device with an Integrated Check Valve for Enhanced Flow Control.

A passive microvalve has appealing advantages in cost-effective and miniaturized microfluidic applications. In this work, we present a passive flow regulatory device for enhanced flow control in a microfluidic environment. The device was integrated with two functional elements, including a flow regulating valve and a flow check valve. Importantly, the flow regulating valve could maintain a stable flow rate over a threshold liquid pressure, and the flow check valve enabled effective liquid on/off control, thus accurate forward flow without any backward leakage was achieved. The flow performance of the flow regulating valve was analyzed through 3D FSI (Fluid-Structure Interaction) simulation, and several key parameters (i.e., fluidic channel height and width, control channel length, and Young’s modulus) were found to influence valve flow rate directly. To examine the flow characteristics of the device, we fabricated a prototype using 3D printing and UV laser cutting technologies, and the flow rates of the prototype under varied test pressures were measured in forward and reverse modes, respectively. Experimental results showed that nearly a constant flow rate of 0.42 ± 0.02 mL s−1 was achieved in the forward mode at an inlet pressure range of 70 kPa to 130 kPa, and liquid flow was totally stopped in the reverse mode at a maximum pressure of 200 kPa. The proposed microfluidic flow regulatory device could be employed for accurate flow control in low-cost and portable Lab-on-a-Chip (LoC) applications.

M86 NOVEL MUTATION IN PPEF2 REPORTED IN A FAMILY AFFECTED WITH SCHIZOPHRENIA: WHOLE GENOME SEQUENCING STUDY

In this paper, cooperative non-orthogonal multiple access (NOMA) network is investigated to aid device-to-device (D2D) communication. In such D2D NOMA, Amplify and Forward (AF) and Decode and Forward (DF) mode are deployed to signal processing at relay who intends to serve NOMA far user. To ensure the quality of service (QoS) for the NOMA devices, a minimum rate requirement is pre-defined for each device. Two main schemes are considered insightfully: i) The first scenario is that the first device intends to communicate with the second device through the assistance of AF/DF-assisted base station (BS), where equips individual power; and ii) The second scenario is that the wireless powered device is able to communicate with non-energy harvesting device. Because of the QoS requirement, it is first necessary to determine performance gap in two folds: relay and direct mode; non-wireless power transfer (NWPT) scenario and wireless power transfer (WPT) scenario, by comparing the outage performance with the required power for satisfying the QoS of the devices. To further evaluation, we extend our analysis on non-linear energy harvesting policy and multiple NOMA far users which are deployed in such D2D transmission. If feasible, a closed-form solution is provided for system performance evaluation. Numerical results are presented to validate the effectiveness of the proposed D2D transmission strategies.

Thermionic emission driven resistive switching behaviour in Ca and Sr doped YMnO3 thin film devices

In this communication, we report the resistive switching (RS) behavior of pulsed laser deposition (PLD) grown with 5% Ca and Sr doped YMnO3 [referred with general formula as Y0.95A0.05MnO3 (YAMO), where A = Ca or Sr; YCMO if A is Ca and YSMO if A = Sr] on (100) single crystalline Nb:SrTiO3 (SNTO) substrates. The thickness of both the YCMO and YSMO thin film devices were ∼300 nm. The hysteretic current–voltage (I–V) characteristics were measured at 100 and 300 K across the YAMO/SNTO interfaces using current perpendicular to plane (CPP) transport measurement geometry. Both these devices exhibit distinct RS behaviours and these are highly influenced by the temperature, ionic size of dopants (i.e. Ca and Sr) and structural disorder as well as lattice mismatch between the films and substrates. While the YCMO/SNTO device exhibits an effective RS behavior in the reverse bias mode, the YSMO/SNTO device in the forward bias mode. The current compliance effects were observed for both the thin film devices and in both the bias modes and their modifications with different parameters. These results are discussed in the light of oxygen vacancies, their distribution and mobility. Thermionic emission model has been employed to understand the charge conduction mechanism across the YAMO/SNTO junctions. The variations in the barrier height has been obtained by fitting the experimental data of I–V with different temperatures, resistance states, dopants and bias modes and discussed in detail. Retention behaviours in the context of switching cycles and time duration have been studied at 100 and 300 K for the verification of device stability, reliability and reproducibility.

Wide-band Beam-scanning by Surface Wave Confinement on Leaky Wave Holograms

A two-dimensional (2-D) metasurface design for backward leaky wave suppression in microwave regime is proposed based on the theory of holography. The so-called Rabbit’s ears phenomenon describes that the backward mode in the reference wave plays the destructive role and makes the holography principle to behave properly mainly in an only narrow frequency interval. Here, we explore the utilization of the surface wave reflectors to suppress the backward mode to achieve wide-band holograms. Therefore, the reference wave form is manipulated by the choice of various reflector shapes and some providing forward mode dominant reference wave are analyzed and simulated. The less backward mode participates in the reference wave; the wider operation frequency range is obtained. With the canceled Rabbit’s ears phenomenon, variations in the reference wave frequency cause elevation angle scan. The results provide general insights into relation of the Rabbit’s ears phenomenon and the object wave accuracy in frequencies except the design frequency. The idea is also applied to multiple object wave holograms. The concept is verified using both electromagnetic full-wave simulations and experimental measurements.

Automatic differentiation using operator overloading (ADOO) for implicit resolution of hyperbolic single phase and two-phase flow models

Implicit time integration schemes are widely used in computational fluid dynamics to speed-up computations. Indeed, implicit schemes usually allow for less stringent time-step stability constraints than their explicit counterpart. The derivation of an implicit scheme is however a challenging and time-consuming task, increasing substantially with the model equations complexity since this method usually requires fairly accurate evaluation of the spatial scheme's matrix Jacobian. This article presents a flexible method to overcome the difficulties associated to the computation of the derivatives, based on the forward mode of automatic differentiation using operator overloading (ADOO). Flexibility and simplicity of the method are illustrated through implicit resolution of various flow models of increasing complexity such as the compressible Euler equations, a two-phase flow model in full equilibrium [28] and a symmetric variant [44] of the two-phase flow model of Baer and Nunziato [2] dealing with mixtures in total disequilibrium.

Theoretical and experimental analysis of a horizontal planar Liquid-Vapour Thermal Diode (PLVTD)

Thermal diodes are unidirectional heat transfer devices, analogous to electrical diodes, which offer low resistance (thermal conductance) in one direction and high resistance (thermal insulation) in the other. Thermal diodicity has significant potential to improve the efficacy of a wide variety of heating and cooling devices. This paper presents pioneering work to experimentally measure the heat transfer characteristics of a 0.15 m2 passive Planar Liquid-Vapour Thermal Diode (PLVTD). Prior work has typically examined much smaller devices aimed at micro-electronics cooling applications whereas the present work aims to improve understanding of larger scale devices for incorporation in solar collectors and multi-function climate control building envelopes. Such applications can facilitate local renewable energy generation (solar and ambient heat collection) and improve cooling system energy efficiency (passive heat rejection) in order to address the climate crisis by decarbonising built environment energy use. Experimental work involved a horizontally oriented PLVTD formed of two parallel isothermal plates with integral serpentine heat exchangers and external insulation. Plate, fluid, and ambient temperatures were controlled and measured to determine heat transfer coefficients under various temperature difference and heat flux operating scenarios in order to validate a simple one-dimensional lumped parameter model. Measured forward mode heat transfer 150 < Uf < 500 W·m−2 K−1 combined with reverse mode insulation Ur = 10 W·m−2 K−1 corresponds ς ≈ 88% diodicity at low condenser temperatures and fluxes (T2 ≈ 15 °C and q/A ≈ 120 W∙m−2) and ς ≈ 96% at high condenser temperatures and heat fluxes (T2 ≈ 60 °C and q/A ≈ 2800 W∙m−2). Forward mode performance increases with increasing heat flux and (to a lesser extent) with increasing operating temperature but is largely independent of PLVTD dimensions. Reverse mode performance is largely independent of heat flux and temperature but reduces (improves thermal insulation) with increasing cavity depth. The model has been used to show that a stainless steel PLVTD with x = 70 mm cavity can achieve Ur = 2 W·m−2 K−1 with similar forward mode performance to the experimental prototype. Such a device would achieve diodicity of ς > 97% and be suitable for application in solar collectors and climate control building envelopes.

The Development of Malaysian Body Somatotype Model using Comprehensive Multivariate Techniques

This study was designed to develop Malaysian body somatotype model among U21 athletes using multivariate analysis. A total of 85 athletes (aged 20.5 ± 5.5 year) were participated in the assessment of anthropometrics measurements. They were from three types of sports which are weightlifter, futsal and Sepak Takraw. These selected sports were represented three categories of body somatotypes namely endomorph, mesomorph and ectomorph respectively. Discriminant Analysis (DA) was used to determine the model and validate the accuracy of these groups classification. As the result, DA obtained 98.8% variability with two factors. First factor (F1) revealed 85.9% discrimination while second factor (F2) revealed 12.9% discrimination as it is related to anthropometrics and the variation of three groups significantly. A body somatotype model was generated using the standardized coefficient of F1. Standard DA showed three discriminated variables (height, sitting height and weight) with 67.06% percentage of correctness. While forward and backward stepwise mode assigned two discriminated variables (weight and height) with 69.41% percentage of correctness. They were established as essential indicators for differentiating body physical category.

Flexible topology converter used in photovoltaic micro‐inverter for higher weighted‐efficiency

This study proposes a pre-stage flexible DC–DC converter (PFDDC) for PV micro-inverter. The PFDDC can be operated in different modes automatically, i.e. the improved full-bridge mode when the output power is higher than the threshold value or in the improved two-transistor forward mode when the output power is lower than the threshold value. The operational principles of the PFDDC in different modes are analysed. The design of the key parameters, such as the turns ratio of transformer and buffering inductance, is presented at first. Then the loss analysis of the PFDDC in different modes is used to determine the threshold power, based on which a switch control strategy according to the threshold power value is proposed. Integration of two operational modes in a single PFDDC can effectively increase the weighted efficiency of the PV micro-inverter to easily satisfy the mandatory efficiency requirement in Europe and USA. Experimental results are presented to verify the effectiveness of the proposed PFDDC.

Study on the Raw Water Allocation and Optimization in Shenzhen City, China

In order to allocate the raw water of the complex water supply system in Shenzhen reasonably, this paper studied the complex network relationship of this large-scale urban water supply system, which consists of 46 reservoirs, 67 waterworks, 2 external diversion water sources, 14 pumping stations and 9 gates, and described each component of the system with the concepts of point, line and plane. Using the topological analysis technology and graph theory, a generalized model of the network topological structure of the urban water allocation system was established. On this basis, combined with the water demand prediction and allocation model of waterworks, a water resources allocation model was established, aiming at satisfying the guaranteed rate of the water supply. The decomposition and coordination principle of the large-scale system and the dynamic simulation technology of the supply-demand balance were adopted to solve the model. The forward calculation mode of controlling waterworks and pumps, and the reverse calculation mode of controlling reservoirs and waterworks were designed in solving the model, and a double-layer feedback mechanism was formed, which took the reverse calculation mode as outer feedback and the reservoir water level constraint or pipeline capacity constraint as inner feedback. Through the verification calculation of the case study, it was found that the proposed model can deal well with the raw water allocation of a large-scale complex water supply system, which had an important application value and a practical significance.

Evaluating the performance of PROSPECT in the retrieval of leaf traits across canopy throughout the growing season

Leaf traits and subsequently leaf spectral properties depend on the leaf phenological stage and light conditions within a canopy. The PROSPECT radiative transfer model has been extensively and successfully used to retrieve leaf traits for mature, sunlit leaves at peak vegetation growth, i.e. summer. However, research on the quantification of leaf traits using PROSPECT across the canopy vertical profile throughout the growing season is still lacking. Therefore, this study aims at examining the effect of leaf position on the performance of the PROSPECT model in modelling leaf optical properties and retrieving leaf chlorophyll content (Cab), equivalent water thickness (EWT), and leaf mass per area (LMA) throughout the growing season. To achieve this objective, we collected 588 leaf samples from the upper and lower canopies of deciduous stands over three seasons (i.e., spring, summer and autumn) in Bavaria Forest National Park, Germany. Leaf traits including Cab, EWT and LMA, were measured for all the samples, and their reflectance spectra were obtained using an ASD FieldSpec-3 Pro FR spectroradiometer coupled with an Integrating Sphere. We initially assessed the performance of the PROSPECT model by comparing reflectance spectra generated in forward mode against reflectance spectra measured on leaf samples collected in the field. We subsequently inverted the PROSPECT model to retrieve Cab, EWT and LMA using the look-up-table (LUT) approach. Our results consistently demonstrated that the measured reflectance of leaf samples collected from the lower canopy had a stronger match with PROSPECT simulated reflectance spectra, especially in the NIR spectrum compared to leaf samples collected from the upper canopy throughout the growing season. This observation concurred with the pattern of Cab and EWT retrieval accuracies across the canopy i.e. the retrieval accuracy for the lower canopy was consistently higher (NRMSE = 0.1-0.2 for Cab; NRMSE = 0.125-0.16 for EWT) when compared to the upper canopy (NRMSE = 0.122 - 0.269 for Cab; NRMSE = 0.162 -0.0.258 for EWT) across all seasons. In contrast, LMA retrieval accuracies for the upper canopy (NRMSE = 0.146 - 0.184) were higher compared to the lower canopy (NRMSE = 0.162 - 0.239) for all seasons except for the spring season. For all the leaf traits examined in this study, the range in retrieval accuracy between the upper and lower canopy was greater in summer (compared to other seasons). We report for the first time that although the PROSPECT model provides reasonable retrieval accuracy of Cab, EWT and LMA, variations in leaf biochemistry and morphology through the vertical canopy profile affects the performance of the model over the growing season. Findings of this study have important implications on field sampling protocols and upscaling leaf traits to canopy and landscape level using multi-layered physical models coupled with PROSPECT.

A comparison of the transport kinetics of glycine transporter 1 and glycine transporter 2.

Transporters of the solute carrier 6 (SLC6) family translocate their cognate substrate together with Na+ and Cl- Detailed kinetic models exist for the transporters of GABA (GAT1/SLC6A1) and the monoamines dopamine (DAT/SLC6A3) and serotonin (SERT/SLC6A4). Here, we posited that the transport cycle of individual SLC6 transporters reflects the physiological requirements they operate under. We tested this hypothesis by analyzing the transport cycle of glycine transporter 1 (GlyT1/SLC6A9) and glycine transporter 2 (GlyT2/SLC6A5). GlyT2 is the only SLC6 family member known to translocate glycine, Na+, and Cl- in a 1:3:1 stoichiometry. We analyzed partial reactions in real time by electrophysiological recordings. Contrary to monoamine transporters, both GlyTs were found to have a high transport capacity driven by rapid return of the empty transporter after release of Cl- on the intracellular side. Rapid cycling of both GlyTs was further supported by highly cooperative binding of cosubstrate ions and substrate such that their forward transport mode was maintained even under conditions of elevated intracellular Na+ or Cl- The most important differences in the transport cycle of GlyT1 and GlyT2 arose from the kinetics of charge movement and the resulting voltage-dependent rate-limiting reactions: the kinetics of GlyT1 were governed by transition of the substrate-bound transporter from outward- to inward-facing conformations, whereas the kinetics of GlyT2 were governed by Na+ binding (or a related conformational change). Kinetic modeling showed that the kinetics of GlyT1 are ideally suited for supplying the extracellular glycine levels required for NMDA receptor activation.

Convergence and error analysis of an automatically differentiated finite volume based heat conduction code

Purpose This paper aims to investigate the convergence and error properties of a finite volume-based heat conduction code that uses automatic differentiation to evaluate derivatives of solutions outputs with respect to arbitrary solution input(s). A problem involving conduction in a plane wall with convection at its surfaces is used as a test problem, as it has an analytical solution, and the error can be evaluated directly. Design/methodology/approach The finite volume method is used to discretize the transient heat diffusion equation with constant thermophysical properties. The discretized problem is then linearized, which results in two linear systems; one for the primary solution field and one for the secondary field, representing the derivative of the primary field with respect to the selected input(s). Derivatives required in the formation of the secondary linear system are obtained by automatic differentiation using an operator overloading and templating approach in C++. Findings The temporal and spatial discretization error for the derivative solution follows the same order of accuracy as the primary solution. Second-order accuracy of the spatial and temporal discretization schemes is confirmed for both primary and secondary problems using both orthogonal and non-orthogonal grids. However, it has been found that for non-orthogonal cases, there is a limit to the error reduction, which is concluded to be a result of errors in the Gauss-based gradient reconstruction method. Originality/value The convergence and error properties of derivative solutions obtained by forward mode automatic differentiation of finite volume-based codes have not been previously investigated.