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1 – 10 of 13Nuan Fang Xu, Zi-Chen Deng, Yan Wang and Kai Zhang
The purpose of this paper is to study the dynamic vibrations of the tethered satellite system (TSS).
Abstract
Purpose
The purpose of this paper is to study the dynamic vibrations of the tethered satellite system (TSS).
Design/methodology/approach
The energy principle and the variational approach are used to establish the dynamic equations of the TSS. By introducing new generalized coordinates, the equations are transformed into the Hamiltonian system. Then, the symplectic Runge-Kutta (SRK) method is used to solve the canonical equations.
Findings
The influence of the tether length on the dynamic behavior of the TSS is very important.
Originality/value
The dynamic responses of the TSS are obtained by using the SRK method.
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Hongwei Yang, Yingying Wang, Meng Zhang and Lianchun Long
This paper aims to provide a symplectic conservation numerical analysis method for the study of nonlinear LC circuit.
Abstract
Purpose
This paper aims to provide a symplectic conservation numerical analysis method for the study of nonlinear LC circuit.
Design/methodology/approach
The flux linkage control type nonlinear inductance model is adopted, and the LC circuit can be converted into the Hamiltonian system by introducing the electric charge as the state variable of the flux linkage. The nonlinear Hamiltonian matrix equation can be solved by perturbation method, which can be written as the sum of linear and nonlinear terms. Firstly, the linear part can be solved exactly. On this basis, the nonlinear part is analyzed by the canonical transformation. Then, the coefficient matrix of the obtained equation is still a Hamiltonian matrix, so symplectic conservation is achieved.
Findings
Numerical results reveal that the method proposed has strong stability, high precision and efficiency, and it has great advantages in long-term simulations.
Originality/value
This method provides a novel and effective way in studying the nonlinear LC circuit.
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Burkhard Göttlicher and Karl Schweizerhof
The computation of structures moving in central force fields generally requires long‐time integration including geometrically nonlinear behavior (large rotations) as such, e.g…
Abstract
The computation of structures moving in central force fields generally requires long‐time integration including geometrically nonlinear behavior (large rotations) as such, e.g. satellite structures move for a long time. To achieve a numerically stable computation the energy momentum method which fulfills linear and angular momentum as well as energy conservation within the time step is chosen for the time integration. The focus in the contribution is on Hamiltonian systems. A formulation for the gravitational force in a central force field as external force on a rigid or flexible satellite is given. The presented formulation enables the computation of the exact spatial distribution of the gravitational forces acting on a structure using the FE‐discretization which is necessary to analyze, e.g. the orientation of a satellite in a gravitational field. The fulfillment of the conservation laws within the time step is proved. The necessity for considering the spatial distribution of the gravitational forces is discussed based on numerical examples.
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Nielen Stander and Erwin Stein
Using examples of flexible mechanisms, demonstrates that while the Newmark method is unstable for nonlinear dynamics, time step refinement could in some cases lead to even earlier…
Abstract
Using examples of flexible mechanisms, demonstrates that while the Newmark method is unstable for nonlinear dynamics, time step refinement could in some cases lead to even earlier onset of instability in the form of a blown‐up response. As a remedy, develops a plane finite beam element based on the Simo‐Vu Quoc formulation for dynamics and integrates it with an energy‐conserving midpoint time‐stepping rule for solving problems in nonlinear dynamics. Shows that this combination produces a consistently stable and accurate dynamic analysis method even for large time steps.
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André Nicolet and Frédéric Zolla
Proposes to posit a clear definition of the energy stored in general electromagnetic media.
Abstract
Purpose
Proposes to posit a clear definition of the energy stored in general electromagnetic media.
Design/methodology/approach
A general setting of thermodynamics using differential geometry is used and it is shown how the Poynting identity fits in.
Findings
A general method of defining the energy storage and dissipation in a general media is stated.
Research limitations/implications
It appears that the definition of the energy stored in a dispersive media is not a state variable and depends on the history of the field variation.
Practical implications
If an electromagnetic model has to be coupled to a mechanical or thermal one, the associated forces and/or heat dissipations may not be clearly defined if one merely knows the electromagnetic constitutive relations.
Originality/value
It proposes a very general setting for the thermodynamic of electrodynamic media.
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D Baldomir and P Hammond
The paper explores the geometrical structure of electrodynamics using the algebra of differential forms. Stokes' theorem links the local to the global geometrical features of…
Abstract
The paper explores the geometrical structure of electrodynamics using the algebra of differential forms. Stokes' theorem links the local to the global geometrical features of electromagnetic systems. The gauge invariance of the potentials is shown to be linked to the geometry of a circle in the complex plane, which exhibits the inner geometry of electrodynamics. The total geometry of a system is a combination of this inner geometry with the usual space‐time geometry. The application of these geometrical features to computation is explained.
Muhammad Naeem Aslam, Arshad Riaz, Nadeem Shaukat, Muhammad Waheed Aslam and Ghaliah Alhamzi
This study aims to present a unique hybrid metaheuristic approach to solving the nonlinear analysis of hall currents and electric double layer (EDL) effects in multiphase wavy…
Abstract
Purpose
This study aims to present a unique hybrid metaheuristic approach to solving the nonlinear analysis of hall currents and electric double layer (EDL) effects in multiphase wavy flow by merging the firefly algorithm (FA) and the water cycle algorithm (WCA).
Design/methodology/approach
Nonlinear Hall currents and EDL effects in multiphase wavy flow are originally described by partial differential equations, which are then translated into an ordinary differential equation model. The hybrid FA-WCA technique is used to take on the optimization challenge and find the best possible design weights for artificial neural networks. The fitness function is efficiently optimized by this hybrid approach, allowing the optimal design weights to be determined.
Findings
The proposed strategy is shown to be effective by taking into account multiple variables to arrive at a single answer. The numerical results obtained from the proposed method exhibit good agreement with the reference solution within finite intervals, showcasing the accuracy of the approach used in this study. Furthermore, a comparison is made between the presented results and the reference numerical solutions of the Hall Currents and electroosmotic effects in multiphase wavy flow problem.
Originality/value
This comparative analysis includes various performance indices, providing a statistical assessment of the precision, efficiency and reliability of the proposed approach. Moreover, to the best of the authors’ knowledge, this is a new work which has not been explored in existing literature and will add new directions to the field of fluid flows to predict most accurate results.
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Masao Shimada, David Tae, Tao Xue, Rohit Deokar and K K Tamma
The purpose of this paper is to present new implementation aspects of unified explicit time integration algorithms, called the explicit GS4-II family of algorithms, of a…
Abstract
Purpose
The purpose of this paper is to present new implementation aspects of unified explicit time integration algorithms, called the explicit GS4-II family of algorithms, of a second-order time accuracy in all the unknowns (e.g. positions, velocities, and accelerations) with particular attention to the moving-particle simulation (MPS) method for solving the incompressible fluids with free surfaces.
Design/methodology/approach
In the present paper, the explicit GS4-II family of algorithms is implemented in the MPS method in the following two different approaches: a direct explicit formulation with the use of the weak incompressibility equation involving the (modified) speed of sound; and a predictor-corrector explicit formulation. The first approach basically follows the concept of the explicit MPS method, presented in the literature, and the latter approach employs a similar concept used in, for example, a fractional-step method in computational fluid dynamics.
Findings
Illustrative numerical examples demonstrate that any scheme within the proposed algorithmic framework captures the physics with the necessary second-order time accuracy and stability.
Originality/value
The new algorithmic framework extended with the GS4-II family encompasses a multitude of pastand new schemes and offers a general purpose and unified implementation.
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Adrien Catella, Victorita Dolean and Stéphane Lanteri
The purpose of this paper is to develop a time implicit discontinuous Galerkin method for the simulation of two‐dimensional time‐domain electromagnetic wave propagation on…
Abstract
Purpose
The purpose of this paper is to develop a time implicit discontinuous Galerkin method for the simulation of two‐dimensional time‐domain electromagnetic wave propagation on non‐uniform triangular meshes.
Design/methodology/approach
The proposed method combines an arbitrary high‐order discontinuous Galerkin method for the discretization in space designed on triangular meshes, with a second‐order Cranck‐Nicolson scheme for time integration. At each time step, a multifrontal sparse LU method is used for solving the linear system resulting from the discretization of the TE Maxwell equations.
Findings
Despite the computational overhead of the solution of a linear system at each time step, the resulting implicit discontinuous Galerkin time‐domain method allows for a noticeable reduction of the computing time as compared to its explicit counterpart based on a leap‐frog time integration scheme.
Research limitations/implications
The proposed method is useful if the underlying mesh is non‐uniform or locally refined such as when dealing with complex geometric features or with heterogeneous propagation media.
Practical implications
The paper is a first step towards the development of an efficient discontinuous Galerkin method for the simulation of three‐dimensional time‐domain electromagnetic wave propagation on non‐uniform tetrahedral meshes. It yields first insights of the capabilities of implicit time stepping through a detailed numerical assessment of accuracy properties and computational performances.
Originality/value
In the field of high‐frequency computational electromagnetism, the use of implicit time stepping has so far been limited to Cartesian meshes in conjunction with the finite difference time‐domain (FDTD) method (e.g. the alternating direction implicit FDTD method). The paper is the first attempt to combine implicit time stepping with a discontinuous Galerkin discretization method designed on simplex meshes.
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The purpose of this paper is to both determine the effects of the nonlinearity on the wave dynamics and assess the temporal and spatial accuracy of five finite difference methods…
Abstract
Purpose
The purpose of this paper is to both determine the effects of the nonlinearity on the wave dynamics and assess the temporal and spatial accuracy of five finite difference methods for the solution of the inviscid generalized regularized long-wave (GRLW) equation subject to initial Gaussian conditions.
Design/methodology/approach
Two implicit second- and fourth-order accurate finite difference methods and three Runge-Kutta procedures are introduced. The methods employ a new dependent variable which contains the wave amplitude and its second-order spatial derivative. Numerical experiments are reported for several temporal and spatial step sizes in order to assess their accuracy and the preservation of the first two invariants of the inviscid GRLW equation as functions of the spatial and temporal orders of accuracy, and thus determine the conditions under which grid-independent results are obtained.
Findings
It has been found that the steepening of the wave increase as the nonlinearity exponent is increased and that the accuracy of the fourth-order Runge-Kutta method is comparable to that of a second-order implicit procedure for time steps smaller than 100th, and that only the fourth-order compact method is almost grid-independent if the time step is on the order of 1,000th and more than 5,000 grid points are used, because of the initial steepening of the initial profile, wave breakup and solitary wave propagation.
Originality/value
This is the first study where an accuracy assessment of wave breakup of the inviscid GRLW equation subject to initial Gaussian conditions is reported.
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