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Time-dependent Problems (time-dependent + problem)
Selected AbstractsMagnetic jets from swirling discsMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 3 2006D. Lynden-Bell ABSTRACT A broad swathe of astrophysical phenomena, ranging from tubular planetary nebulae through Herbig,Haro objects, radio galaxy and quasar emissions to gamma-ray bursts and perhaps high-energy cosmic rays, may be driven by magnetically dominated jets emanating from accretion discs. We give a self-contained account of the analytic theory of non-relativistic magnetically dominated jets wound up by a swirling disc and making a magnetic cavity in a background medium of any prescribed pressure, p(z). We solve the time-dependent problem for any specified distribution of magnetic flux P(R, 0) emerging from the disc at z= 0, with any specified disc angular velocity ,d(R). The physics required to do this involves only the freezing of the lines of force to the conducting medium and the principle of minimum energy. In a constant pressure environment, the magnetically dominated cavity is highly collimated and advances along the axis at a constant speed closely related to the maximum circular velocity of the accretion disc. Even within the cavity the field is strongly concentrated towards the axis. The twist in the jet field ,B,,/,|Bz|, is close to and the width of the jet decreases upwards. By contrast, when the background pressure falls off with height with powers approaching z,4, the head of the jet accelerates strongly and the twist of the jet is much smaller. The width increases to give an almost conical magnetic cavity with apex at the source. Such a regime may be responsible for some of the longest strongly collimated jets. When the background pressure falls off faster than z,4, there are no quasi-static configurations of well-twisted fields and the pressure confinement is replaced by a dynamic effective pressure or a relativistic expansion. In the regimes with rapid acceleration, the outgoing and incoming fields linking the twist back to the source are almost anti-parallel so there is a possibility that magnetic reconnections may break up the jet into a series of magnetic ,smoke-rings' travelling out along the axis. [source] Starting solutions for the boundary immobilization methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 6 2005J. Caldwell Abstract The boundary immobilization method (BIM) is extended to the cases of outward spherical and cylindrical solidifications, which involves the development of starting solutions. When applying the method to time-dependent problems, good agreement is achieved when comparing the positions of the moving boundary and the temperature distribution with those obtained by the perturbation method. Copyright © 2004 John Wiley & Sons, Ltd. [source] A new hybrid velocity integration method applied to elastic wave propagationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2008Zhiyun Chen Abstract We present a novel space,time Galerkin method for solutions of second-order time-dependent problems. By introducing the displacement,velocity relationship implicitly, the governing set of equations is reformulated into a first-order single field problem with the unknowns in the velocity field. The resulting equation is in turn solved by a time-discontinuous Galerkin approach (Int. J. Numer. Anal. Meth. Geomech. 2006; 30:1113,1134), in which the continuity between time intervals is weakly enforced by a special upwind flux treatment. After solving the equation for the unknown velocities, the displacement field quantities are computed a posteriori in a post-processing step. Various numerical examples demonstrate the efficiency and reliability of the proposed method. Convergence studies with respect to the h - and p -refinement and different discretization techniques are given. Copyright © 2007 John Wiley & Sons, Ltd. [source] Design spaces, measures and metrics for evaluating quality of time operators and consequences leading to improved algorithms by design,illustration to structural dynamicsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2005X. Zhou Abstract For the first time, for time discretized operators, we describe and articulate the importance and notion of design spaces and algorithmic measures that not only can provide new avenues for improved algorithms by design, but also can distinguish in general, the quality of computational algorithms for time-dependent problems; the particular emphasis is on structural dynamics applications for the purpose of illustration and demonstration of the basic concepts (the underlying concepts can be extended to other disciplines as well). For further developments in time discretized operators and/or for evaluating existing methods, from the established measures for computational algorithms, the conclusion that the most effective (in the sense of convergence, namely, the stability and accuracy, and complexity, namely, the algorithmic formulation and algorithmic structure) computational algorithm should appear in a certain algorithmic structure of the design space amongst comparable algorithms is drawn. With this conclusion, and also with the notion of providing new avenues leading to improved algorithms by design, as an illustration, a novel computational algorithm which departs from the traditional paradigm (in the sense of LMS methods with which we are mostly familiar with and widely used in commercial software) is particularly designed into the perspective design space representation of comparable algorithms, and is termed here as the forward displacement non-linearly explicit L-stable (FDEL) algorithm which is unconditionally consistent and does not require non-linear iterations within each time step. From the established measures for comparable algorithms, simply for illustration purposes, the resulting design of the FDEL formulation is then compared with the commonly advocated explicit central difference method and the implicit Newmark average acceleration method (alternately, the same conclusion holds true against controllable numerically dissipative algorithms) which pertain to the class of linear multi-step (LMS) methods for assessing both linear and non-linear dynamic cases. The conclusions that the proposed new design of the FDEL algorithm which is a direct consequence of the present notion of design spaces and measures, is the most effective algorithm to-date to our knowledge in comparison to the class of second-order accurate algorithms pertaining to LMS methods for routine and general non-linear dynamic situations is finally drawn through rigorous numerical experiments. Copyright © 2005 John Wiley & Sons, Ltd. [source] Automatic energy conserving space,time refinement for linear dynamic structural problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2005P. Cavin Abstract In this paper a local space,time automatic refinement method (STAR method) is developed to efficiently solve time-dependent problems using FEM techniques. The automatic process is driven by an energy or a displacement error indicator which controls the precision of the result. The STAR method solves the numerical problem on grids with different mesh size. For the Newmark schemes, a general demonstration, using the energy method, gives the interface conditions between two successive grids which is compatible with the stability of the scheme. Finally, using a linear one-dimensional example, the convergence of the method and the precision of the results are discussed. Copyright © 2005 John Wiley & Sons, Ltd. [source] Anisotropic mesh adaption for time-dependent problems,INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9 2008S. Micheletti Abstract We propose a space,time adaptive procedure for a model parabolic problem based on a theoretically sound anisotropic a posteriori error analysis. A space,time finite element scheme (continuous in space but discontinuous in time) is employed to discretize this problem, thus allowing for non-matching meshes at different time levels. Copyright © 2008 John Wiley & Sons, Ltd. [source] On hybrid quantum,classical transport modelsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 6 2004Naoufel Ben Abdallah Abstract This paper contains a review on the coupling between classical models and quantum models for electron transport in semiconductors. Starting from the quantum analogue of the boundary value problem for the Vlasov equation, the coupling with the Boltzmann equation in the one-dimensional stationary situation is reviewed for the stationary and time-dependent problems. Then a numerical scheme based on the characteristics method is applied to the stationary hybrid model. Some mathematical properties of the scheme are proven and illustrated in some numerical experiments. Copyright © 2004 John Wiley & Sons, Ltd. [source] A numerical study of the accuracy and stability of symmetric and asymmetric RBF collocation methods for hyperbolic PDEsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2008Scott A. Sarra Abstract Differentiation matrices associated with radial basis function (RBF) collocation methods often have eigenvalues with positive real parts of significant magnitude. This prevents the use of the methods for time-dependent problems, particulary if explicit time integration schemes are employed. In this work, accuracy and eigenvalue stability of symmetric and asymmetric RBF collocation methods are numerically explored for some model hyperbolic initial boundary value problems in one and two dimensions. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008 [source] | |||||||||||||