FORTRAN Algorithm Research Articles

Numerical Analysis of Magnetic Field Effect on Ferro Particle Suspended Nanofluid Filled Square Enclosure Consist of Heat Generating Body

In presents of a magnetic field, an enclosure filled with ferro-particle suspended nanofluid is subjected to a numerical analysis to investigate natural convective heat transfer. At the center of the enclosure is a heat conducting and generating solid body, and the enclosure is influenced by four different thermal boundary conditions. To solve the governing equation, a Fortran algorithm based on the finite volume approach was created. The numerical approach used in this study produces consistent results for a variety of non-dimensional parameters like Rayleigh number (104 ≤ Ra ≤ 106), Hartmann number (0 ≤ Ha ≤ 100), solid volume fraction (0 ≤ φ ≤ 0.2) and distributed wall temperature. Streamlines, isotherms, and the Nusselt number graph are used to describe the flow and heat transfer properties. Based on this study, It has been noted that improved heat transfer for lower Hartmann number with higher Rayleigh number particularly along sinusoidal wall. For the low Hartmann number, the fluid flow enhances for higher Rayleigh number. In particular, the presence of ferro-particle suspended nanofluid enhances the heat transfer rate. Moreover, this study has found that the inclusion of magnetic fields and nanoparticles can increase heat transfer by up to 60%. The suggested methods in this research can assist manufacturers improve efficiency without increasing heat generator space in industrial applications for cooling or heating.

Experimental Study and Modeling of a Convective Dryer for Fruits and Vegetables

The present work deals with the study of the thermal performances of a convective dryer for fruits and vegetables. This dryer, operating with energy generated from the combustion of biomass in a boiler connected to a water/air heat exchanger could be a solution to the problematic of energy related to drying. An experimental and theoretical study is carried out on the temperature profile inside the dryer. For this purpose, 10.3 kg of tomatoes were dried on the experimental setup. The operation lasted about 16 hours and reduced the moisture content from 93.8% to 12% in wet basis. The overall thermal efficiency of the convective dryer during the trial is 10.76%. For the theoretical study, the dryer components (boiler, water/air exchanger and drying chamber) are first modeled individually; the different sub-programs are then coupled to form the convective dryer program. The method of global heat balances combined with the one called “ε-NUT” is used. The set of equations is discretized using the implicit method of finite differences, then solved with the Gauss algorithm in Fortran 90. The theoretical results obtained are in good agreement with those measured.

SolveSAPHE-r2 (v2.0.1): revisiting and extending the Solver Suite for Alkalinity-PH Equations for usage with CO<sub>2</sub>, HCO<sub>3</sub><sup>−</sup> or CO<sub>3</sub><sup>2−</sup> input data

Abstract. The successful and efficient approach at the basis of the Solver Suite for Alkalinity-PH Equations (SolveSAPHE) (Munhoven, 2013), which determines the carbonate system speciation by calculating pH from total alkalinity (AlkT) and dissolved inorganic carbon (CT), and which converges for any physically sensible pair of such data, has been adapted and further developed to work with AlkT–CO2, AlkT–HCO3-, and AlkT–CO32-. The mathematical properties of the three modified alkalinity–pH equations are explored. It is shown that the AlkT–CO2, and AlkT–HCO3- problems have one and only one positive root for any physically sensible pair of data (i.e. such that [CO2]>0 and [HCO3-]>0). The space of AlkT–CO32- pairs is partitioned into regions where there is either no solution, one solution or where there are two. The numerical solution of the modified alkalinity–pH equations is far more demanding than that for the original AlkT–CT pair as they exhibit strong gradients and are not always monotonous. The two main algorithms used in SolveSAPHE v1 have been revised in depth to reliably process the three additional data input pairs. The AlkT–CO2 pair is numerically the most challenging. With the Newton–Raphson-based solver, it takes about 5 times as long to solve as the companion AlkT–CT pair; the AlkT–CO32- pair requires on average about 4 times as much time as the AlkT–CT pair. All in all, the secant-based solver offers the best performance. It outperforms the Newton–Raphson-based one by up to a factor of 4 in terms of average numbers of iterations and execution time and yet reaches equation residuals that are up to 7 orders of magnitude lower. Just like the pH solvers from the v1 series, SolveSAPHE-r2 includes automatic root bracketing and efficient initialisation schemes for the iterative solvers. For AlkT–CO32- data pairs, it also determines the number of roots and calculates non-overlapping bracketing intervals. An open-source reference implementation of the new algorithms in Fortran 90 is made publicly available for usage under the GNU Lesser General Public Licence version 3 (LGPLv3) or later.

RISK ASSESSMENT OF THERMAL DAMAGE TO PEOPLE AT INDUSTRIAL SITES IN CASE OF EMERGENCY BURNING SOLID PROPELLANT

Purpose. This work involves the development of a numerical model for the calculation of areas of thermal damage to people in the event of solid propellant burning at the industrial site. Methodology. An equation expressing the law of energy conservation was used to solve the problem of determining the areas of thermal shock of people at the industrial site. A potential flow model was used to calculate the airflow velocity field in the presence of buildings at the industrial site where an emergency occurs. The numerical solution of the two-dimensional equation for the velocity potential is derived using the Liebmann method. This numerical model takes into account the uneven velocity field of the wind flow that is formed near industrial buildings. An implicit difference splitting scheme was used to numerically solve the energy equation. The physical splitting of a two-dimensional energy equation into a system of one-dimensional equations describing the temperature transfer in one coordinate direction has been carried out previously. At each splitting step, the unknown temperature value is determined by an explicit point-to-point computation scheme. Based on the numerical model built, the code using the FORTRAN algorithm language is created. Findings. Based on the developed numerical model, a computational experiment was conducted to evaluate the risk of thermal damage to people at the industrial site where solid propellants are produced. The dangerous areas for personnel are identified. Originality. An efficient numerical model has been developed to calculate the zones of thermal pollution in case of solid propellant burning. Practical value. Based on the developed mathematical model, a computer program was created, which allows performing serial calculations for determining the zones of thermal damage during emergencies at the chemically hazardous objects. The mathematical model developed can be used to design an emergency response plan for chemically hazardous objects.

PYMIEDAP: a Python–Fortran tool for computing fluxes and polarization signals of (exo)planets

PYMIEDAP (the Python Mie Doubling-Adding Programme) is a Python-based tool for computing the total linearly and circularly polarized fluxes of incident unpolarized sunlight or starlight that is reflected by solar system planets or moons, respectively, or by exoplanets at a range of wavelengths. The radiative transfer computations are based on an doubling-adding Fortran algorithm and fully include polarization for all orders of scattering. The model (exo)planets are described by a model atmosphere composed of a stack of homogeneous layers containing gas and/or aerosol and/or cloud particles bounded below by an isotropically depolarizing surface (that is optionally black). The reflected light can be computed spatially resolved and/or disk-integrated. Spatially resolved signals are mostly representative for observations of solar system planets (or moons), while disk-integrated signals are mostly representative for exoplanet observations. PYMIEDAP is modular and flexible, and allows users to adapt and optimize the code according to their needs. PYMIEDAP keeps options open for connections with external programs and for future additions and extensions. In this paper, we describe the radiative transfer algorithm that PYMIEDAP is based on and the principal functionalities of the code. We also provide benchmark results of PYMIEDAP that can be used for testing its installation and for comparison with other codes.

A Pilot Climate Sensitivity Study Using the CEN Coupled Adjoint Model (CESAM)

A pilot coupled climate sensitivity study is presented based on the newly developed adjoint coupled climate model, Centrum für Erdsystemforschung und Nachhaltigkeit (CEN) Earth System Assimilation Model (CESAM). To this end the components of the coupled forward model are summarized, and the generation of the adjoint code out of the model forward code through the application of the Transformation of Algorithms in FORTRAN (TAF) adjoint compiler is discussed. It is shown that simulations of the intermediate-complexity CESAM are comparable in quality to CMIP-type coupled climate models, justifying the usage of the model to compute adjoint sensitivities of the northern Europe near-surface temperature to anomalies in surface temperature, sea surface salinity, and sea ice over the North Atlantic and the Arctic on time scales of up to one month. Results confirm that on a time scale of up to a few days surface temperatures over northern Europe are influenced by Atlantic temperature anomalies just upstream of the target location. With increasingly longer time lapse, however, it is the influence of SSTs over the central and western North Atlantic on the overlying atmosphere and the associated changes in storm-track pattern that dominate the evolution of the surface European temperature. Influences of surface salinity and sea ice on the northern European temperature appear to have similar sensitivity mechanisms, invoked indirectly through their influence on near-surface temperature anomalies. The adjoint study thus confirms that the SST’s impact on the atmospheric dynamics, notably storm tracks, is the primary cause for the influence of northern European temperature changes.

The development of GPU-based parallel PRNG for Monte Carlo applications in CUDA Fortran

The implementation of Monte Carlo simulation on the CUDA Fortran requires a fast random number generation with good statistical properties on GPU. In this study, a GPU-based parallel pseudo random number generator (GPPRNG) have been proposed to use in high performance computing systems. According to the type of GPU memory usage, GPU scheme is divided into two work modes including GLOBAL_MODE and SHARED_MODE. To generate parallel random numbers based on the independent sequence method, the combination of middle-square method and chaotic map along with the Xorshift PRNG have been employed. Implementation of our developed PPRNG on a single GPU showed a speedup of 150x and 470x (with respect to the speed of PRNG on a single CPU core) for GLOBAL_MODE and SHARED_MODE, respectively. To evaluate the accuracy of our developed GPPRNG, its performance was compared to that of some other commercially available PPRNGs such as MATLAB, FORTRAN and Miller-Park algorithm through employing the specific standard tests. The results of this comparison showed that the developed GPPRNG in this study can be used as a fast and accurate tool for computational science applications.

An innovative nanofluid-based cooling using separated natural and forced convection in low Reynolds flows

This article numerically studies the thermal performance of a cavity filled with the alumina-water nanofluid and with a discrete heat source at its bottom. The cavity is located on the bottom wall of a horizontal channel; and it is cooled by an external air flow entering the channel with a low Reynolds number and a temperature relatively lower than the heat source temperature. The significance of this study is the unique heat transfer mechanism due to both forced convection of main fluid in the channel and natural convection of nanofluid within the cavity without any mixing between forced and natural convection. The pertinent parameters analysed in this study are the Reynolds number of main fluid in the channel (1≤Re≤20), the Rayleigh number (104≤Ra≤107) and the solid volume fraction of alumina-water nanofluid (0≤ϕ≤0.04) in the cavity. A numerical model was generated to simulate the forced convection in the channel, heat conduction in the cavity walls and the natural convection in the cavity. The corresponding governing equations were solved using the SIMPLE algorithm in Fortran. The results were presented in terms of flow and temperature patterns, velocity profile at different cross-sections of the channel and the local and average Nusselt numbers. It was found that the proposed cooling method was effective in removing heat from the heat source and the heat transfer rate increased at higher Reynolds and Rayleigh numbers. It was also found that the nanofluid with a higher solid volume fraction corresponds to a higher heat transfer rate; the rate of heat transfer increase, however, was less pronounced at Ra = 105 compared to other values of Rayleigh number.

Adjoint of the global Eulerian–Lagrangian coupled atmospheric transport model (A-GELCA v1.0): development and validation

Abstract. We present the development of the Adjoint of the Global Eulerian–Lagrangian Coupled Atmospheric (A-GELCA) model that consists of the National Institute for Environmental Studies (NIES) model as an Eulerian three-dimensional transport model (TM), and FLEXPART (FLEXible PARTicle dispersion model) as the Lagrangian Particle Dispersion Model (LPDM). The forward tangent linear and adjoint components of the Eulerian model were constructed directly from the original NIES TM code using an automatic differentiation tool known as TAF (Transformation of Algorithms in Fortran; http://www.FastOpt.com), with additional manual pre- and post-processing aimed at improving transparency and clarity of the code and optimizing the performance of the computing, including MPI (Message Passing Interface). The Lagrangian component did not require any code modification, as LPDMs are self-adjoint and track a significant number of particles backward in time in order to calculate the sensitivity of the observations to the neighboring emission areas. The constructed Eulerian adjoint was coupled with the Lagrangian component at a time boundary in the global domain. The simulations presented in this work were performed using the A-GELCA model in forward and adjoint modes. The forward simulation shows that the coupled model improves reproduction of the seasonal cycle and short-term variability of CO2. Mean bias and standard deviation for five of the six Siberian sites considered decrease roughly by 1 ppm when using the coupled model. The adjoint of the Eulerian model was shown, through several numerical tests, to be very accurate (within machine epsilon with mismatch around to ±6 e−14) compared to direct forward sensitivity calculations. The developed adjoint of the coupled model combines the flux conservation and stability of an Eulerian discrete adjoint formulation with the flexibility, accuracy, and high resolution of a Lagrangian backward trajectory formulation. A-GELCA will be incorporated into a variational inversion system designed to optimize surface fluxes of greenhouse gases.

Real-time Capable Nonlinear Model Predictive Controller Design for the Upper Stage of a Launch Vehicle

In this paper, a real-time capable Nonlinear Model Predictive Controller (NMPC) is implemented for the attitude control of an upper stage launch vehicle with liquid propellant. A mass spring model is used as an analogy to simulate the disturbance generated by the sloshing propellant. For the implementation of the NMPC, an optimal control problem (OCP) is defined with finite time horizon. The objective function is minimized while satisfying constraints on the control inputs. The resulting OCP is transcribed using single shooting method to parametrize the control inputs using uniform discretization points. The continuous control inputs are obtained by linear interpolation. A dedicated discretization algorithm in FORTRAN is coupled with a solver which used quasi-Newton algorithm to generate solutions fast. Approximation of the Hessian matrix is used to reduce computational requirements. Furthermore, the algorithm can perform parallel computation of the derivatives of the objective function with respect to optimization variables. This results in a real-time capability of generating solutions in the order of milliseconds for each iteration. The algorithm is applied for attitude maneuver and disturbance rejection for the upper stage of a launch vehicle.

The efficiency of geophysical adjoint codes generated by automatic differentiation tools

The accuracy of numerical models that describe complex physical or chemical processes depends on the choice of model parameters. Estimating an optimal set of parameters by optimization algorithms requires knowledge of the sensitivity of the process of interest to model parameters. Typically the sensitivity computation involves differentiation of the model, which can be performed by applying algorithmic differentiation (AD) tools to the underlying numerical code. However, existing AD tools differ substantially in design, legibility and computational efficiency. In this study we show that, for geophysical data assimilation problems of varying complexity, the performance of adjoint codes generated by the existing AD tools (i) Open_AD, (ii) Tapenade, (iii) NAGWare and (iv) Transformation of Algorithms in Fortran (TAF) can be vastly different. Based on simple test problems, we evaluate the efficiency of each AD tool with respect to computational speed, accuracy of the adjoint, the efficiency of memory usage, and the capability of each AD tool to handle modern FORTRAN 90–95 elements such as structures and pointers, which are new elements that either combine groups of variables or provide aliases to memory addresses, respectively. We show that, while operator overloading tools are the only ones suitable for modern codes written in object-oriented programming languages, their computational efficiency lags behind source transformation by orders of magnitude, rendering the application of these modern tools to practical assimilation problems prohibitive. In contrast, the application of source transformation tools appears to be the most efficient choice, allowing handling even large geophysical data assimilation problems. However, they can only be applied to numerical models written in earlier generations of programming languages. Our study indicates that applying existing AD tools to realistic geophysical problems faces limitations that urgently need to be solved to allow the continuous use of AD tools for solving geophysical problems on modern computer architectures.

On the Mechanism of Corrosion in Presence of Organic Acids

Theories on the role of organic acids in general, and acetic acid in particular, in carbon steel corrosion were initiated in 1940s with the reports on the significant effect of acetic acid in pipeline corrosion in oil and gas industry1. It was reported that even small amounts of acetic acid (300 ppm) can cause severe corrosion of pipeline steel1. Later on, several studies on the concentration of organic acids in formation water of oil and gas wells have been reported up to 3000 ppm of acetic acid1–4. Despite numerous studies on the mechanism of acetic acid corrosion of pipeline steel, details of the mechanism are still debated. Acetic acid is known as a week acid which is partially dissociate in water. It is also known that weak acids act as a reservoir for hydrogen ions in the corrosion process. This phenomenon known as “buffering effect”, describes the enhanced limiting current in presence of acetic acid compared to the case of strong acids at a similar pH. Additionally, it is suggested that the undissociated acetic acid is also a proton donor and is able to be reduced at the surface of the steel, which is known as “direct reduction” mechanism. The direct reduction mechanism has been used for years5,6. Also, many other studies on the combined effect of acetic acid and carbon dioxide on carbon steel have adopted the same mechanism7–9. However, recent studies suggest that undissociated acetic acid is only involved in the corrosion process as a buffer for hydrogen ions. Tran et al.10 report a series of polarization curves on SS304 stainless steel, showing that the concentration of acetic acid does not affect the charge transfer portion of the cathodic sweeps. Therefore, they have concluded that acetic acid is not involved in charge transfer processes directly and that the buffering effect is the main mechanism. In that study, authors suggest that the same mechanism is valid for carbon steel. In the present study an iron electrode was used instead of carbon steel in order to minimize the effect of impurities such as carbon. Figure 1 presents the experimental data collected in the present work and the comparison with the results of the mathematical simulations. The experimental data are collected using a rotating disk electrode made from pure iron exposed in a two liter, three electrode glass cell in deoxygenated aqueous solution. The mathematical simulation is the solution of Nernst Plank equation for an acetic acid aqueous system. These equations are solved with finite difference method, using Newman’s BANDJ11 algorithm in FORTRAN with a MATLAB user interface. Figure 1 shows a clear linear cathodic charge transfer behavior at both pH values. Additionally the charge transfer part of the cathodic reactions is insensitive to changes in concentration of acetic acid which is the indication that free acetic acid in the system is not directly reduced at the surface of iron. Current results confirm that the proposed mechanism by Tran et al. applies to pure iron which has great similarity to pipeline steel. The mathematical calculations proposed here also support the same conclusion. Additionally, comparison of the calculated charge transfer rates based on these results suggests that the rate of dissolution of iron is slightly retarded in presence of acetic acid.

Numerical Model for Analysis in Space Radiators for Critical Conditions Operating

Satellites, normally, are subject to large variations in temperature due to its orbit. On the other hand, the equipment that make up feature limits (minimum and maximum) of temperature must not be exceeded so that the satellite's operation is not compromised. In this way, this paper presents a numerical comparison between a plane radiator and finned radiator in critical operating conditions. Designed to operate in passive thermal control of satellites, these devices reject the heat generated by electronic components and minimize the absorption of heat from external sources (especially the sun) in order to maintain the temperature of the satellite components within their operating ranges. For this purpose, two algorithms in Fortran® were developed for solving the nonlinear system of equations which govern the conductive-radioactive coupling in both radiators. These equations were discretized by two-dimensional Finite Volume Method and the resulting system was solved with the application of Tri-Diagonal Matrix Algorithm combined with an iterative process. The numerical obtained results show the temperature profiles to both radiators studied in critical operation conditions.

Kinetics of Biochar Liquefaction

The renewable resource pyrolysis char hereinafter often referred to as biochar, produced by pyrolysis or hydrothermal carbonization, has promising properties for advanced upgrade. Technologies for the conversion of biochar to biofuels may therefore contribute to suffice the growing demand for fuel. Direct liquefaction of biochar is a conceivable way of producing biofuels. Direct liquefaction of biochar was carried out in a 450 ml batch reactor at a temperature of 425 °C with the hydrogen donor solvent tetralin. Biochar conversion of 84 % and an oil yield of 72 % were observed after 33 min of reaction time. Compared to fossil coal liquefaction, the hydrogenation of biochar leads to a diverse product distribution with more oil products and less intermediates. In process modeling, intermediates as well as products and residues of similar product properties according to their solubility in different organic solvents were identified. These product classes formed the basis for investigation of kinetics of biochar liquefaction. The reaction route network resulting from the reaction scheme was solved with a FORTRAN algorithm.

Mathematics of the total alkalinity–pH equation – pathway to robust and universal solution algorithms: the SolveSAPHE package v1.0.1

Abstract. The total alkalinity–pH equation, which relates total alkalinity and pH for a given set of total concentrations of the acid–base systems that contribute to total alkalinity in a given water sample, is reviewed and its mathematical properties established. We prove that the equation function is strictly monotone and always has exactly one positive root. Different commonly used approximations are discussed and compared. An original method to derive appropriate initial values for the iterative solution of the cubic polynomial equation based upon carbonate-borate-alkalinity is presented. We then review different methods that have been used to solve the total alkalinity–pH equation, with a main focus on biogeochemical models. The shortcomings and limitations of these methods are made out and discussed. We then present two variants of a new, robust and universally convergent algorithm to solve the total alkalinity–pH equation. This algorithm does not require any a priori knowledge of the solution. SolveSAPHE (Solver Suite for Alkalinity-PH Equations) provides reference implementations of several variants of the new algorithm in Fortran 90, together with new implementations of other, previously published solvers. The new iterative procedure is shown to converge from any starting value to the physical solution. The extra computational cost for the convergence security is only 10–15% compared to the fastest algorithm in our test series.

Data Analysis and Result Computation (DARC) Algorithm for Tertiary Institutions

Tertiary institutions (e.g., Universities, Polytechnics and Colleges of Education) are expected to manage and preserve data of both present and past students. These data include general information about students as well as examination results at any or all stages of studentship. Analysis of student data can be used to inform solutions to a wide variety of educational challenges like exploring group differences, gender representation, ethnic representation, and growth over time. However, data management and examination result computation of large population of students can be rigorous time-consuming and prone to errors. Information management technology offers a comprehensive portfolio of students’ academic record to be available in real-time to students and professionals. That a comprehensive solution for use in many tertiary institutions is not yet common presents a unique opportunity for researchers to help shape the future of this technology. We introduce a Fortran algorithm for Data Analysis and Result Computation (DARC). The algorithm analyzes student data as well as computes examination results of all students in a department at once. DARC reads particular spreadsheet formats of students’ information data, semester scores and previous academic records, after which it outputs, among others, analysis of students information, comprehensive result format for students showing grade point averages(GPA) and updated cumulative grade point averages (CGPA), summary of academic records including log of carry over courses, log of carry over courses that have been cleared, log of outstanding courses and log of outstanding courses that have been cleared. Using synthetic record of some students, we validate the reliability of the algorithm by conducting accuracy tests. The algorithm is flexible and can be suitably modified to manage and preserve academic and general records of both present and past students in any tertiary institution.

Algorithm 923

Computing the Pfaffian of a skew-symmetric matrix is a problem that arises in various fields of physics. Both computing the Pfaffian and a related problem, computing the canonical form of a skew-symmetric matrix under unitary congruence, can be solved easily once the skew-symmetric matrix has been reduced to skew-symmetric tridiagonal form. We develop efficient numerical methods for computing this tridiagonal form based on Gaussian elimination, using a skew-symmetric, blocked form of the Parlett-Reid algorithm, or based on unitary transformations, using block Householder transformations and Givens rotations, that are applicable to dense and banded matrices, respectively. We also give a complete and fully optimized implementation of these algorithms in Fortran (including a C interface), and also provide Python, Matlab and Mathematica implementations for convenience. Finally, we apply these methods to compute the topological charge of a class D nanowire, and show numerically the equivalence of definitions based on the Hamiltonian and the scattering matrix.

Application of an Adiabatic WRF Adjoint to the Investigation of the May 2004 McMurdo, Antarctica, Severe Wind Event

The tangent linear and adjoint of an adiabatic version of the Weather Research and Forecasting (WRF) Model with its Advanced Research WRF (ARW) dynamic core have been developed. The source-to-source automatic differentiation tool [i.e., the Transformation of Algorithm (TAF) in FORTRAN] was used in the development. Tangent linear and adjoint checks of the developed adiabatic WRF adjoint modeling system (WAMS) were conducted, and all necessary correctness verification procedures were passed. As the first application, the adiabatic WAMS was used to study the adjoint sensitivity of a severe windstorm in Antarctica. Linearity tests indicated that an adjoint-based sensitivity study with the Antarctic Mesoscale Prediction System (AMPS) 90-km domain configuration for the windstorm is valid up to 24 h. The adjoint-based sensitivity calculation with adiabatic WAMS identified sensitive regions for the improvement of the 24-h forecast of the windstorm. It is indicated that the windstorm forecast largely relies on the model initial conditions in the area from the south part of the Trans-Antarctic Mountains to West Antarctica and between the Ross Ice Shelf and the South Pole. Based on the sensitivity analysis, the southerly or southeasterly wind at lower levels in the sensitivity region should be larger, the cyclone should be stronger, and the atmospheric stratification should be more stable over the north slope of the Trans-Antarctic Mountain to the Ross Ice Shelf, than the AMPS analyses. By constructing pseudo-observations in the sensitivity region using the gradient information of forecast windstorm intensity around McMurdo, the model initial conditions are revised with the WRF three-dimensional variational data assimilation, which leads to significant improvement in the prediction of the windstorm. An adjoint sensitivity study is an efficient way to identify sensitivity regions in order to collect more observations in the region for better forecasts in a specific aspect of interest.

Software developed for obtaining GPS‐derived total electron content values

This paper describes a complex technique with its built‐in cycle slip correction procedures that have been developed for ionospheric space research to obtain high‐quality and high‐precision GPS‐derived total electron content (TEC) values. Thus, to correct GPS anomalies while the signatures of space weather features detected in the dual‐frequency 30‐s rate GPS data are preserved is the main aim of this technique. Its main requirement is to complete fully automatically all the tasks required to turn the observational data to the desired final product. Its major tasks include curve fitting, cycle slip detection and correction in the slant relative TEC data, residual error detection and correction in the vertical TEC data, and vertical TEC data filtering for quantifying data smoothness and GPS phase fluctuations. A detailed description of these two data correction methods is given. Validation tests showing weaknesses and strengths of the methods developed are also included and discussed. Versatility and accuracy of the methods are demonstrated with interesting and real‐world examples obtained from smooth midlatitude and from dynamic low‐ and high‐latitude data. Results indicate that errors can be detected and corrected more reliably in the vertical TEC data than in the slant TEC data because of the lower rate of change of vertical TEC over a 30‐s sampling period. Future work includes the development of a complex software package wherein the individual FORTRAN algorithms, described in this paper, will be incorporated into one main (FORTRAN, Matlab, or C++) program to provide professional and customized GPS data processing for ionospheric space research.

Discrete Adjoint Approach for Modeling Unsteady Aerodynamic Design Sensitivities

A discrete adjoint approach is presented for computing steady and unsteady aerodynamic design sensitivities for compressible viscous flows about airfoil configurations. The nominal flow solver method is based on a harmonic balance solution technique, which is capable of modeling both steady and nonlinear periodic unsteady flows. The computer code for the discrete adjoint solver, which is derived from the nominal harmonic balance solver, has been generated with the aid of the advanced automatic differentiation software tool known as TAF (Transformation of Algorithms in FORTRAN).