Study of an implicit scheme for integrating Maxwell's equations

We study theoretically and numerically an implicit scheme for solving Maxwell's equations. Space discretization is obtained by the finite element method, while Newmark's scheme provides the time discretization.     

Computations of steady,ellipsoidal vortex rings with finite cores

A numerical study of vortex rings of ellipsoidal shape is presented that have finite cores and are solution to the Navier-Stokes equations. The cross section of the core of the vortex ring is non-circular and is a result of the numerical solution described in the paper. The cross-sectional shape is defined by the strength of the vorticity distribution in the core and by the axis ratio of the ellipsoid, defining the outer dimensions of the vortex ring. Hill's spherical vortex and O'Brien's ellipsoidal vortices are limiting cases of the vortex rings described in this paper.     

A Comparative analysis of Green’s functions of 1D matching equations for motion synthesis

When filtering an input image, the Green’s functions of matching equations are capable of inducing a broad class of motions, a property that has led to their use in several computer graphics and computer vision applications. In all such applications, the Green’s functions of second-order differential equations have been considered, even though no justification has been given for their preference over simpler, first-order equations. Here we present a study of first-order one-dimensional matching equations, both in the uniform and in the affine motion models. Comparing their Green’s functions with those of the corresponding second-order cases, we find evidence for the latter’s superiority in motion synthesis. We also propose and discuss a general discretization scheme for Green’s functions of one-dimensional matching equations, showing that the affine motion model is particularly sensitive to the sampling frequency. In this case, we advocate the use of area sampling, for allowing realistic motion simulations.     

Iterative methods for the solution of the navier equations of elasticity

The numerical solution of the Navier equations discretized by finite elements is studied by various forms of pre-conditioned conjugate gradient methods. In particular, the dependence of the number of iterations is examined as a function of Poisson's ratio. A comparison is made with direct solution methods, and the dependence of the discretization error on Poisson's ratio is also discussed.     

On multi-rigid-body system dynamics

A computer-oriented method for obtaining dynamical equations of motion for large mechanical systems or “chain systems” is presented. A chain system is defined as an arbitrarily assembled set of rigid bodies such that adjoining bodies have at least one common point and such that closed loops are not formed. The equations of motion are developed through the use of Lagrange's form of d'Alembert's principle.The method has been applied with human-body models and finite-segment cable models. The numan-body models are configured to simulate a crash-victim. Results obtained with several deceleration profiles agree very well with available experimental data.     

Higher order methods for convection-diffusion problems

This paper applies C¹ cubic Hermite polynomials embedded in an orthogonal collocation scheme to the spatial discretization of the unsteady nonlinear Burgers equation as a model of the equations of fluid mechanics. The temporal discretization is carried out by means of either a noniterative finite difference or an iterative finite difference procedure. Results of this method are compared with those of a second-order finite difference scheme and a splined-cubic Taylor's series scheme. Stability limits are derived and the matrix structure of the several schemes are compared.     

A finite element penalty method for the linearized viscoelastic Oldroyd fluid motion equations

In this paper, a fully discrete finite element penalty method is considered for the two-dimensional linearized viscoelastic fluid motion equations, arising from the Oldroyd model for the non-Newton fluid flows. With the finite element method for the spatial discretization and the backward Euler scheme for the temporal discretization, the velocity and pressure are decoupled in this method, which leads to a large reduction of the computational scale. Under some realistic assumptions, the unconditional stability of the fully discrete scheme is proved. Moreover, the optimal error estimates are obtained, which are better than the existing results. Finally, some numerical results are given to verify the theoretical analysis. The difference between the motion of the Newton and non-Newton fluid is also observed.     

Multibody structural dynamics including translation between the bodies

New and recently developed concepts useful for obtaining and solving equations of motion of multibody mechanical systems with translation between the respective bodies of the system, is presented. The incorporation of translation effects make the analysis applicable to a much broader class of problems than was possible with previous analyses which are restricted to linked multibody systems.The concepts developed in the analysis include the use of Euler parameters, Lagrange's form of d'Alembert's principle, quasi-coordinates, relative coordinates, and body connection arrays. Procedures for the development of efficient computer algorithms for evaluating the coefficients of the governing equations of motion are outlined.The methods presented are directly applicable in the analysis of biodynamic and human models, finite segment cable models, mechanisms, manipulators and robots.     

A study of suspended roofs for near-source seismic motions

The non-linear behavior of multi-suspended roof systems for seismic loads is studied. The study is based on a formulation that can be easily employed for a preliminary design of multi-suspended roofs subjected to seismic loads. Specifically, applying Lagrange’s equations, the corresponding set of equations of motion for discrete models of multiple suspension roofs is obtained and numerical integration of the equations of motion is performed via the Runge–Kutta scheme. For representative realistic combinations of geometric, stiffness and damping parameters, a non-linear analysis is employed to study the behavior of suspended roofs for near-source and far-field seismic motions. The analysis demonstrates that: (i) code-specified design loads could dramatically underestimate the response of suspended roofs subjected to near-source ground motions and (ii) flexible roofing systems are greatly affected by near-source ground motions, a behavior that is not observed for stiff systems.     

Energy Stability Analysis of Some Fully Discrete Numerical Schemes for Incompressible Navier–Stokes Equations on Staggered Grids

In this paper we consider the energy stability estimates for some fully discrete schemes which both consider time and spatial discretizations for the incompressible Navier–Stokes equations. We focus on three kinds of fully discrete schemes, i.e., the linear implicit scheme for time discretization with the finite difference method (FDM) on staggered grids for spatial discretization, pressure-correction schemes for time discretization with the FDM on staggered grids for the solutions of the decoupled velocity and pressure equations, and pressure-stabilization schemes for time discretization with the FDM on staggered grids for the solutions of the decoupled velocity and pressure equations. The energy stability estimates are obtained for the above each fully discrete scheme. The upwind scheme is used in the discretization of the convection term which plays an important role in the design of unconditionally stable discrete schemes. Numerical results are given to verify the theoretical analysis.     

Application of the Petrov-Galerkin method to chemical-flooding reservoir simulation in one dimension

A one-dimensional, chemical-flooding simulator is described. This program models the effect that polymers, surfactants and salts have on the enhanced recovery of oil. The flow equations are convection dominated and often shock-like profiles develop which traverse the domain. The simulator incorporates, with a few modifications, most of the physical and chemical package which is set forth by Pope and Nelson. The spacial discretization is performed via the Petrov-Galerkin, finite element method. This technique is mainly derived from the work of Hughes and Brooks and is modified for the case of chemical flooding. We compare this finite element method to the upstream, finite difference method and to Galerkin's method. Generally speaking, the Petrov-Galerkin results are significantly less sensitive to the number of grid points than are those of the upstream method. Its stability properties are nearly the same as those of the upstream techniques, which in turn, are superior to those of Galerkin's method.     

Dynamics of shells of revolution under axisymmetric load involving shear deformation

A general solution procedure, based on the linear theory, is presented for arbitrary shells of revolution subjected to arbitrary axisymmetric dynamic loads. The equations of motion admit shear deformation and rotational inertia. The numerical solution is obtained by Houbolt's method and by finite differences.     

Elastic Plates in Multibody Systems: A Treatment Using Existing Rigid Body Codes

In the present paper, it is shown how one can employ existing rigid body codes to handle systems containing elastic plates by using a Rayleigh–Ritz discretization procedure. The equations of motion are formulated for a rectangular plate undergoing large rigid body motions but small elastic deformations. Geometric nonlinearities in the elastic coordinates are taken into account to include the effect of dynamic stiffening. As an example, a spin-up maneuver for a simply-supported plate is treated.     

On the influence of shape and dimensions of particles on the properties of the modified particle-in-cell method

It is considered Harlow's particle-in-cell method modification which consists in the use of finite-size particles for two dimensional gasdynamics computations. The algorithm for computation of motion of finite size particles is described. It is shown that the use of finite size particles can lead to the local violation of the approximation of original differential equations. However the quantities obtained by averaging the numerical solution over certain spatial subdomains approximate the conservation laws. It is shown that if the characteristic particle dimensions tend to zero, then themodified particle-in-cell method passes to the original Harlow's method. Results of numerical experiments are given to illustrate the properties of the modified particle-in-cell method.     

A distributed parameter model for the dynamics of flexible-link robots

In this paper a model is developed for kinematic and dynamic analysis of flexible robots undergoing general three-dimensional motion. For modeling robotic links, distributed mass and flexibility are considered without discretization. Some modeling issues are discussed, and parameters characterizing the real design of a robot are introduced into the analysis. The concept of a fictitious rigid link is presented to consider the rigid body motion of a link separately, and to account for possibly complex link shapes. Based on Jourdain's principle, an alternative formulation is proposed to derive the dynamic equations of flexible robots. The equations of motion are developed and analyzed in detail. The vibrations of links are described by linear, inhomogeneous partial differential equations, with homogeneous, nonlinear, time-dependent boundary conditions. © 1998 John Wiley & Sons, Inc.     

Numerical modelling of pulsar magnetospheres

Numerical models used in the study of the pulsar magnetosphere are described: a vacuum model based only on Maxwell's equations and a more realistic model employing both Maxwell's and relativistic two-fluid equations. The general approach to solving the chosen sets of partial differential equations is outlined and the possible boundary conditions are examined. Numerical methods suitable for solving Maxwell's equations are discussed and a method is developed for solving the combined fluid plus Maxwell model. Results are presented and discussed and the possible improvements in the approach are indicated.     

A Partitioned finite element method for dynamical systems

A new analytical method is described for deriving the equations of motion of dynamical systems. The concept is to consider the displacements of the domain to be composed of rigid and elastic components. In contrast to other reduction methods, the domain modeled by finite number of degrees of freedom is discretized into two distinctive types of subdomains. Rigid and elastic subdomains are generated by consistent lumping of the domain properties under unique kinematic constraint relations. Equations of motion of the disjoint subdomains are derived by Lagrange's equations, in conjunction with the shape function matrix represented in partitioned form. This allows reduced sizes of matrices and avoids their possible singularities. Based on the invariance of energies under a compatible partitioned procedure, a simple analytical method is introduced for building the equations of motion of the whole domain from those of the subdomains. The dynamic analysis of a two-node domain with application to a blade-shaft combination is presented to illustrate the method.     

Finite element analysis of long-period water waves

The finite element representation of the nonlinear equations governing the unsteady flow of the two-dimensional long-period shallow water wave is considered. The approximate solution assumes, that the flow is only a slight perturbation of an existing flow. With this assumption a finite element formulation in terms of discrete nodal values of velocity and water height is generated using Galerkin's method. The resulting matrix equation for an arbitrary triangular-based space-time element constitutes a set of linear algebraic equations solvable for nodal values of the flow variables. The topological properties of estuaries are treated and with the solution thus obtained, numerical results are shown for the North Sea.     

A new ship's auto pilot design through a stochastic model

A new type of ship's autopilot system is designed by a statistical approach. A ship's motion at sea is described by a multi-variable autoregressive model using minimum AIC (Akaike's Information Criterion) procedure. Through the fitted model, the ship's behavior is analyzed and an optimal control law for a ship under a newly introduced criterion function is derived. The feasibility of our control system is checked by both digital and hybrid simulations. The results of the simulation show that with our controller the yaw motion is depressed through smoother and less rudder motion than that of the conventional autopilot systems and the ill effect of rolling is avoided. It is expected that the controller has another merit: it is quite robust for possible changes of external environments. Finally, a successful result of an actual sea test is briefly discussed. Thus, the possibility of realizing an entirely new autopilot system by a stochastic model is demonstrated.