Split Boundary Research Articles

Mancha3D Code: Multipurpose Advanced Nonideal MHD Code for High-Resolution Simulations in Astrophysics

The Mancha3D code is a versatile tool for numerical simulations of magnetohydrodynamic (MHD) processes in solar/stellar atmospheres. The code includes nonideal physics derived from plasma partial ionization, a realistic equation of state and radiative transfer, which allows performing high-quality realistic simulations of magnetoconvection, as well as idealized simulations of particular processes, such as wave propagation, instabilities or energetic events. The paper summarizes the equations and methods used in the Mancha3D (Multifluid (-purpose -physics -dimensional) Advanced Non-ideal MHD Code for High resolution simulations in Astrophysics 3D) code. It also describes its numerical stability and parallel performance and efficiency. The code is based on a finite difference discretization and a memory-saving Runge–Kutta (RK) scheme. It handles nonideal effects through super-time-stepping and Hall diffusion schemes, and takes into account thermal conduction by solving an additional hyperbolic equation for the heat flux. The code is easily configurable to perform different kinds of simulations. Several examples of the code usage are given. It is demonstrated that splitting variables into equilibrium and perturbation parts is essential for simulations of wave propagation in a static background. A perfectly matched layer (PML) boundary condition built into the code greatly facilitates a nonreflective open boundary implementation. Spatial filtering is an important numerical remedy to eliminate grid-size perturbations enhancing the code stability. Parallel performance analysis reveals that the code is strongly memory bound, which is a natural consequence of the numerical techniques used, such as split variables and PML boundary conditions. Both strong and weak scalings show adequate performance up to several thousands of processors (CPUs).

Robust Optimal Output-Tracking Control of Constrained Mechanical Systems With Application to Autonomous Rovers

This article presents a robust optimal output-tracking control strategy for underactuated mechanical systems whose motion is restricted by mixed holonomic and nonholonomic constraints. Autonomous rovers/cars and unmanned underwater/aerial vehicles are a few examples of such systems that must often operate in harsh environments and under uncertain conditions. We present a comprehensive control analysis of this large class of nonlinear systems, including the existing studies on local reachability and static state feedback linearization. We also propose a local observability analysis of the feedback transformed input–output linearized systems. Based on the input–output linearization of the holonomically restricted nominal system, we develop a sliding mode control strategy that is robust against the projected effects of uncertainties and disturbances on the system’s output. Asymptotic stability of the output toward a bounded desired trajectory is proven using Lyapunov’s direct method, while the system’s internal stability (in the sense of boundedness) is investigated based on the notion of tracking-error zero dynamics. Time-dependent bounded matched uncertainties in the inertia parameters and disturbance forces arising in the unrestricted system are considered in this study. We propose an optimal sliding manifold according to the finite-horizon linear-quadratic regulator design problem with split boundary value conditions. The developed control strategy is implemented on a six-wheel autonomous Lunar rover in a simulation environment and its performance is compared with that of an optimal proportional–integral–derivative feedback, feedforward controller. The optimal sliding mode controller shows superior performance in trajectory tracking with acceptable control actions.

Acoustic radiation force of a sphere with a hemispherically split boundary condition in a plane wave

In this paper, an analytical expression of the acoustic radiation force (ARF) for a spherical particle with a hemispherically split impedance boundary in a plane wave is deduced. Numerical calculations are carried out by considering the effect of the magnitude and phase of the acoustic impedance on the ARF. Computation results show that the increase in the magnitude of the acoustic impedance results in an overall decrease in the ARF, whereas the phase of the acoustic impedance results in a decrease in the ARF in the low frequency region. As the frequency increases, the positive phase angle leads to a decrease in the ARF, and the negative phase angle causes the ARF to increase rapidly. For a hemispherically split impedance sphere, the values of the ARF range from those of the rigid sphere and uniform impedance sphere. The finite-element models for the calculation of the ARF of a hemispherically split impedance boundary sphere are established and the correctness of the analytical theory is proved by numerical comparison. This work is expected to contribute theoretical support to the acoustic manipulation of particles with a nonuniform hemispherically split structure.

A numerical iterative method for solving two-point BVPs in infinite-horizon nonzero-sum differential games: Economic applications

In this work, the Nash equilibrium solution of nonlinear infinite-horizon nonzero-sum differential games with open-loop information is investigated numerically. For this class of games, some difficulties are involved in finding an open-loop Nash equilibrium. For instance, we must solve a nonlinear differential equations system with split boundary conditions, namely the two-point boundary value problem (TPBVP), in which some of the boundary conditions are specified at the initial time and some at the infinite final time. In the current study, we provide a combined numerical algorithm based on a new set of basis functions on the half-line, called the exponential Chelyshkov functions (ECFs), and quasilinearization (QL) method to solve TPBVPs. In the first step, we reduce the nonlinear TPBVP to a sequence of linear differential equations by using the QL method. Although we have now a linearized system, another difficulty is finding the approximate solution of this linear system such that the transversality conditions at the infinite final time are satisfied. So, in the second step, we apply a collocation method based on the ECFs to solve the obtained linear system in the semi-infinite domain. The convergence of the proposed method is discussed in detail. To confirm the validity and efficiency of the proposed scheme, we compute the approximate solution of TPBVP as well as the open-loop Nash equilibrium for four applications of differential games in economics and management science.

Solvability of a mixed problem for a hyperbolic equation with splitting boundary conditions in the case of incomplete system of eigenfunctions

Solvability of a mixed problem for a hyperbolic equation with splitting boundary conditions in the case of incomplete system of eigenfunctions

A numerical algorithm to find optimum parameters of a flexible-link manipulator arm for performing payload launching

PurposeThe aim of the current study is proposing a novel framework to attain the optimum value of a flexible arm manipulator parameters for payload launching missions.Design/methodology/approachThe proposed scheme is based on optimal control approach and combines direct and indirect search methods while considering the actuator capacity.FindingsThree nonlinear parameter-optimization problems will be solved to illustrate how the proposed algorithm can be exploited. Employing variational based nonlinear optimal control within the suggested framework, the answer of these problems is highly intertwined to the solution of a set of differential equations with split boundary values. To solve the obtained boundary value problem (BVP), the related solver of MATLAB® software, bvp6c, will be employed. The achieved simulation results support the worth of the developed procedure.Originality/valueFor the first time, the optimal parameters of a flexible link robot for object launching are found in the current research. In addition, the actuator saturation limits are considered which enhances the applicability of the suggested method in the real world applications.

Numerical solution of two-point BVPs in infinite-horizon optimal control theory: a combined quasilinearization method with exponential Bernstein functions

ABSTRACT This study is aimed to relate nonlinear infinite-horizon optimal control problems (NLIHOCPs) with open-loop information. The difficulties of solving the two-point boundary value problems (TPBVPs) arising from NLIHOCPs can be assigned to the nonlinearity of differential equations, the combination of split boundary conditions, and how the transversality conditions in infinite-horizon are treated. In this paper, we propose a combined quasilinearization method (QLM) with the exponential Bernstein functions (EBFs) for solving nonlinear TPBVPs on the semi-infinite domain. First, the QLM is used to reduce the nonlinear TPBVP to a sequence of linear differential equations. Then, a collocation method based on the EBFs is utilized to find the approximate solution of the resulting linear differential equations. By applying the EBFs, the transversality conditions for TPBVP on the semi-infinite domain are satisfied. The convergence of the QLM + EBFs is proved. Some numerical experiments are performed to confirm the validity of the proposed computational scheme.

Natural gas treatment by membrane-case study of liquefied natural gas plant of Arzew-Algeria

A calculation method for predicting the performances of multi-component gas mixture through a membrane permeator is presented. Two mathematical models are developed to study the effect of the circulation of feed and permeate inside the membrane module. The explored circulation modes are the cocurrent and the countercurrent flow pattern. The developed mathematical model in the case of countercurrent flow pattern is subject to the split boundary value problem. To solve this problem, a numerical approach is developed combining the (0, 2) Jacobi multi-wavelets method and the decoupling and quasi-linearisation iterative technique. The developed models are then used to predict the performances of a membrane module designed for the treatment of a natural gas load (case study of the liquefied natural gas plant of Arzew-Algeria). The obtained results show clearly the efficiency of the countercurrent compared to the cocurrent flow pattern: high product purity is obtained for the same recovery rate. [Received: May 6, 2019; Accepted: August 7, 2020]

Natural gas treatment by membrane-case study of liquefied natural gas plant of Arzew-Algeria

A calculation method for predicting the performances of multi-component gas mixture through a membrane permeator is presented. Two mathematical models are developed to study the effect of the circulation of feed and permeate inside the membrane module. The explored circulation modes are the cocurrent and the countercurrent flow pattern. The developed mathematical model in the case of countercurrent flow pattern is subject to the split boundary value problem. To solve this problem, a numerical approach is developed combining the (0, 2) Jacobi multi-wavelets method and the decoupling and quasi-linearisation iterative technique. The developed models are then used to predict the performances of a membrane module designed for the treatment of a natural gas load (case study of the liquefied natural gas plant of Arzew-Algeria). The obtained results show clearly the efficiency of the countercurrent compared to the cocurrent flow pattern: high product purity is obtained for the same recovery rate. [Received: May 6, 2019; Accepted: August 7, 2020]

Land use induced blurring of forest-grassland transition in north-west Himalaya — A case study using Moving Split Window boundary detection technique

Transition zone or ecotone is a unique community sandwiched between two communities/ecosystems/biomes. These ecotones in Himalaya remained unexplored for many ecological aspects like biodiversity, phyto-sociology, boundary detection and even impact of change in land use pattern (anthropogenic activity). The most accepted and widespread technique called as Moving Split Window (MSW) technique is used for detection of vegetation and environmental boundaries at four different sites in the lesser stratum of north-west Himalaya. All the four sites were at different distances from the nearest human inhabited area. Anthropogenic activities like grazing, herb collection, wood collection etc. were common at proximal sites. Such activities have led to the change in land use pattern. In this study, we have tried to work out the impact of the change in land use pattern (human interference) on the vegetation and basic environmental parameters like soil pH, electrical conductivity and moisture on forest-grassland ecotone in north-west Himalaya. Data on mountain steepness was also collected and analyzed. The dissimilarity profile using the statistical tool Squared Euclidian Distance (SED) indicated that species turnover locations increase with the increase in distance of ecotones from human settlements. The ecotones at distant locations from human villages are characterized with blunt as well as sharp peaks for vegetation data, however, conditions are reverse in case of the proximal sites. The study also reveals that as the distance between the ecotone and human settlements increases, the complex conditions like multiple vegetation boundaries prevails on the transitions. In this regard, land use induced blurring of forest-grassland transition in north-west Himalaya is summed up in the study.

Evolution of {0kl} 〈1 0 0〉 texture and microstructure in preparation of ultra-thin grain-oriented silicon steel

In this paper, an ultra-thin grain-oriented silicon steel (UTGO steel) strip was prepared via rolling a commercial glassless grain-oriented silicon steel plate to 0.075 mm and then annealing it at 850 °C for less than 30 min in a protective atmosphere. The resultant UTGO steel strip has magnetic induction B800 higher than 1.80 T and iron loss P1.5/400 lower than 12.0 W/kg. These superior magnetic properties are due to predominant {0kl} 〈1 0 0〉 texture and appropriate microstructure. The study shows that preferential {0kl} 〈1 0 0〉 nucleation occurs either inside shear bands or at in-grain deformation-induced boundaries. The nucleation behavior varies at different nucleation sites. Nuclei inside shear bands are denser and show preferential transitional orientation along {0kl} 〈1 0 0〉, while new grains dispersed at in-grain split boundaries have shown orientations which are suggested to inherit corresponding initial grain orientation prior to rolling. Nucleation behavior is also highly dependent on the orientation of the roll-deformed matrix. Our study finds that shear banding nucleation of {0kl} 〈1 0 0〉 (including Goss and {0 2 1} 〈1 0 0〉) is reduced when the orientation of the deformed matrix deviates from {1 1 1} 〈1 1 2〉. With the extension of annealing time, the growth of {0kl} 〈1 0 0〉 nuclei in cluster is restricted because of orientation pinning effect, whereas the growth of grains with orientations other than {0kl} 〈1 0 0〉 is promoted. This phenomenon weakens the dominance of {0kl} 〈1 0 0〉 texture, causing deterioration in magnetic properties of the final silicon steel.

Non-Split PML Boundary Condition for Finite Element Time-Domain Modeling of Ground Penetrating Radar

As a highly efficient absorbing boundary condition, Perfectly Matched Layer (PML) has been widely used in Finite Difference Time Domain (FDTD) simulation of Ground Penetrating Radar (GPR) based on the first order electromagnetic wave equation. However, the PML boundary condition is difficult to apply in GPR Finite Element Time Domain (FETD) simulation based on the second order electromagnetic wave equation. This paper developed a non-split perfectly matched layer (NPML) boundary condition for GPR FETD simulation based on the second order electromagnetic wave equation. Taking two-dimensional TM wave equation as an example, the second order frequency domain equation of GPR was derived according to the definition of complex extending coordinate transformation. Then it transformed into time domain by means of auxiliary differential equation method, and its FETD equation is derived based on Galerkin method. On this basis, a GPR FETD forward program based on NPML boundary condition is developed. The merits of NPML boundary condition are certified by compared with wave field snapshots, signal and reflection errors of homogeneous medium model with split and non-split PML boundary conditions. The comparison demonstrated that the NPML algorithm can reduce memory occupation and improve calculation efficiency. Furthermore, numerical simulation of a complex model verifies the good absorption effects of the NPML boundary condition in complex structures.

Effects of triceps surae muscle strength and tendon stiffness on the reactive dynamic stability and adaptability of older female adults during perturbed walking

This study aimed to examine whether the triceps surae (TS) muscle-tendon unit (MTU) mechanical properties affect gait stability and its reactive adaptation potential to repeated perturbation exposure in older adults. Thirty-four older adults each experienced eight separate unexpected perturbations during treadmill walking, while a motion capture system was used to determine the margin of stability (MoS) and base of support (BoS). Ankle plantar flexor muscle strength and Achilles tendon (AT) stiffness were analyzed using ultrasonography and dynamometry. A median split and separation boundaries classified the subjects into two groups with GroupStrong ( n = 10) showing higher ankle plantar flexor muscle strength (2.26 ± 0.17 vs. 1.47 ± 0.20 N·m/kg, means ± SD; P < 0.001) and AT stiffness (544 ± 75 vs. 429 ± 86 N/mm; P = 0.004) than GroupWeak ( n = 12). The first perturbation caused a negative ΔMoS (MoS in relation to unperturbed baseline walking) at touchdown of perturbed step (PertR), indicating an unstable position. GroupStrong required four recovery steps to return to ΔMoS zero level, whereas GroupWeak was unable to return to baseline within the analyzed steps. However, after repeated perturbations, both groups increased ΔMoS at touchdown of PertR with a similar magnitude. Significant correlations between ΔBoS and ΔMoS at touchdown of the first recovery step and TS MTU capacities (0.41 < r < 0.57; 0.006 < P < 0.048) were found. We conclude that older adults with TS muscle weakness have a diminished ability to control gait stability during unexpected perturbations, increasing their fall risk, but that degeneration in muscle strength and tendon stiffness may not inhibit the ability of the locomotor system to adapt the reactive motor response to repeated perturbations. NEW & NOTEWORTHY Triceps surae muscle weakness and a more compliant Achilles tendon partly limit older adults' ability to effectively enlarge the base of support and recover dynamic stability after an unexpected perturbation during walking, increasing their fall risk. However, the degeneration in muscle strength and tendon stiffness may not inhibit the ability of the locomotor system to adapt the reactive motor response to repeated perturbations.

Angle Control-Based Multi-Terminal Out-of-Step Protection System

From time to time a sequence of unexpected and overlapping contingencies may lead to power system angular instability and even blackouts if not addressed adequately by means of an out-of-step (OOS) protection system. The motivation of the paper is an attempt to develop a workable prototype of the OOS protection system. The deficiencies of the protection currently used in the Latvian Power System network are highlighted and a new protection structure is proposed. The protection system comprises of several strategically located terminals, exchanging information in real time by means of a communication network. The OOS condition detection method is based on system-wide generation sources, electromotive forces, vectors, and angle control. The network splitting decision is based on generator coherence evaluation. Protection terminals determine online the groups of coherent generators and choose the splitting boundary from a predefined transmission lines (TLs) cut sets list. The protection system structure, algorithm of operation, and possible IEC 61850 communication standard-based implementation are described.

Application of shifted Jacobi pseudospectral method for solving (in)finite-horizon min–max optimal control problems with uncertainty

ABSTRACTThe difficulty of solving the min–max optimal control problems (M-MOCPs) with uncertainty using generalised Euler–Lagrange equations is caused by the combination of split boundary conditions, nonlinear differential equations and the manner in which the final time is treated. In this investigation, the shifted Jacobi pseudospectral method (SJPM) as a numerical technique for solving two-point boundary value problems (TPBVPs) in M-MOCPs for several boundary states is proposed. At first, a novel framework of approximate solutions which satisfied the split boundary conditions automatically for various boundary states is presented. Then, by applying the generalised Euler–Lagrange equations and expanding the required approximate solutions as elements of shifted Jacobi polynomials, finding a solution of TPBVPs in nonlinear M-MOCPs with uncertainty is reduced to the solution of a system of algebraic equations. Moreover, the Jacobi polynomials are particularly useful for boundary value problems in unbounded domain, which allow us to solve infinite- as well as finite and free final time problems by domain truncation method. Some numerical examples are given to demonstrate the accuracy and efficiency of the proposed method. A comparative study between the proposed method and other existing methods shows that the SJPM is simple and accurate.

An algorithm for dynamic object manipulation by a flexible link robot

Purpose – The purpose of this paper is to focus on an online closed-loop (CL) approach for performing dynamic object manipulation (DOM) by a flexible link manipulator. Design/methodology/approach – Toward above goal, a neural network and optimal control are integrated in a closed-loop structure, to achieve a robust control for online DOM applications. Additionally, an elegant novel numerical solution method will be developed which can handle the split boundary value problem resulted from DOM mission requirements for a wide range of boundary conditions. Findings – The obtained simulation results reveal the effectiveness of both proposed innovative numerical solution technique and control structure for online object manipulation purposes using flexible manipulators. Originality/value – The object manipulation problem has previously been studied, however, for the first time its accomplishment by flexible link manipulators was addressed just in offline form considering an open-loop control structure (Tarvirdizadeh and Yousefi-Koma, 2012). As an extension of Tarvirdizadeh and Yousefi-Koma (2012), the current research, consequently, focusses on a numerical solution and a CL approach for performing DOM by a flexible link manipulator.

Two-stage controlled islanding strategy based on Stoer-Wagner and improved Dinic algorithms

The controlled islanding for the power system is an effective method to deal with the emergent situations caused by large disturbances. The size of the solution space would increase exponentially as the scale of the power grid increases. The goal of our controlled islanding strategy is to divide the system into several islands quickly. Meanwhile, the generator coherency and the power-flow disruption have to be taken into consideration carefully. This paper proposed a two-stage fast islanding strategy for large power networks, which is on the basis of large power grid graph theories. In the first stage, the Stoer-Wagner algorithm is employed to obtain the grouping cluster of coherent generators in the dynamic undirected liaison graph. In the second stage, the improved Dinic max-flow method is proposed to search the optimal splitting boundary so as to acquire the minimum power flow impact. Our two-stage islanding strategy does not need to reduce the whole power network. Simulations on IEEE 118-bus and 162-bus power systems showed that the proposed strategy can acquire high quality solutions effectively and efficiently.

Robustness of three-phase equilibrium calculations

Phase equilibrium calculations converge less often as the number of phases and components increase, and for overall compositions closer to phase split boundaries and critical points. Computational speed and robustness of flash calculations are very important aspects for pipeline transmission and for reservoir simulation where billions of flash calculations may be done. Reduced methods have the potential to improve the robustness of phase equilibrium calculations because if chosen properly they can linearize the equations, use fewer independent variables and can be unbounded. Improved robustness could further improve the speed and accuracy of compositional simulation and avoid false two-phase solutions, where three or more phases may be present. In this paper, we use the reduced variables of Gorucu and Johns (2014) to test robustness in performing two- and three-phase stability analysis and corresponding flash calculations. These multi-phase equilibrium calculations are compared with the conventional phase equilibrium calculations based on minimization of Gibbs energy and the reduced method proposed by Okuno et al. (2010a). Using thousands of equally-spaced and unbiased multi-phase equilibrium calculations, the proposed multi-phase equilibrium calculations are shown to be more robust than the other two tested algorithms.

Chebyshev orthogonal collocation technique to solve transport phenomena problems with Matlab® and Mathematica

ABSTRACTWe present in this pedagogical paper an alternative numerical method for the resolution of transport phenomena problems encountered in the teaching of the required course on transport phenomena in the graduate chemical engineering curricula. Based on the Chebyshev orthogonal collocation technique implemented in Matlab® and Mathematica©, we show how different rather complicated transport phenomena problems involving partial differential equations and split boundary value problems can now readily be mastered. A description of several sample problems and the resolution methodology is discussed in this paper. The objective of the incorporation of this approach is to develop the numerical skills of the graduate students at King Fahd University of Petroleum &amp; Minerals (KFUPM) and to broaden the extent of transport‐phenomena problems that can be addressed in the course. We noted with satisfaction that the students successfully adopted this numerical technique for the resolution of problems assigned as term projects. © 2014 Wiley Periodicals, Inc. Comput Appl Eng Educ 23:422–431, 2015; View this article online at wileyonlinelibrary.com/journal/cae; DOI 10.1002/cae.21612

Modeling and computer simulation of a reverse osmosis desalination plant—case study of Bousfer plant—Algeria

ABSTRACT This work aims to verify the effects of the retentate and the permeate flow pattern and the concentration polarization phenomenon on the performances of a reverse osmosis desalination plant. The two types of flow circulation studied in this work are the co-current and counter-current flow patterns. Two mathematical models were developed. They are both based on the solution diffusion model. The first mathematical model is formed of a set of non-linear equations. The second one is formed of a set of ordinary differential equations. The numerical resolution of the second mathematical model is subjected to the split boundary value problem. A robust and efficient iterative procedure was developed to solve this problem. It consists in combining the orthogonal collocation and the finite elements method. The non-linear coupled system of differential equations is transformed to an uncoupled linear system by an iterative technique. This linearization allows more stability. The real case of reverse osmosis ...