Home  About us  Contact
 

Time Integrator (time + integrator)

Distribution by Scientific Domains
Engineering100%

Selected Abstracts

Electron transport enhanced molecular dynamics for metals and semi-metals,

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8-9 2010
Reese E. Jones
Abstract In this work we extend classical molecular dynamics by coupling it with an electron transport model known as the two temperature model. This energy balance between free electrons and phonons was first proposed in 1956 by Kaganov et al. but has recently been utilized as a framework for coupling molecular dynamics to a continuum description of electron transport. Using finite element domain decomposition techniques from our previous work as a basis, we develop a coupling scheme that preserves energy and has local control of temperature and energy flux via a Gaussian isokinetic thermostat. Unlike the previous work on this subject, we employ an efficient, implicit time integrator for the fast electron transport which enables larger stable time steps than the explicit schemes commonly used. A number of example simulations are given that validate the method, including Joule heating of a copper nanowire and laser excitation of a suspended carbon nanotube with its ends embedded in a conducting substrate. Published in 2010 by John Wiley & Sons, Ltd. [source]

An implicit edge-based ALE method for the incompressible Navier,Stokes equations,

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2003
Richard W. Smith
Abstract A new finite volume method for the incompressible Navier,Stokes equations, expressed in arbitrary Lagrangian,Eulerian (ALE) form, is presented. The method uses a staggered storage arrangement for the pressure and velocity variables and adopts an edge-based data structure and assembly procedure which is valid for arbitrary n-sided polygonal meshes. Edge formulas are presented for assembling the ALE form of the momentum and pressure equations. An implicit multi-stage time integrator is constructed that is geometrically conservative to the precision of the arithmetic used in the computation. The method is shown to be second-order-accurate in time and space for general time-dependent polygonal meshes. The method is first evaluated using several well-known unsteady incompressible Navier,Stokes problems before being applied to a periodically forced aeroelastic problem and a transient free surface problem. Published in 2003 by John Wiley & Sons, Ltd. [source]

LS-DYNA and the 8:1 differentially heated cavity

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2002
Mark A. Christon
Abstract This paper presents results computed using LS-DYNA's new incompressible flow solver for a differentially heated cavity with an 8:1 aspect ratio at a slightly super-critical Rayleigh number. Three Galerkin-based solution methods are applied to the 8:1 thermal cavity on a sequence of four grids. The solution methods include an explicit time-integration algorithm and two second-order projection methods,one semi-implicit and the other fully implicit. A series of ad hoc modifications to the basic Galerkin finite element method are shown to result in degraded solution quality with the most serious effects introduced by row-sum lumping the mass matrix. The inferior accuracy of a lumped mass matrix relative to a consistent mass matrix is demonstrated with the explicit algorithm which fails to obtain a transient solution on the coarsest grid and exhibits a general trend to under-predict oscillation amplitudes. The best results are obtained with semi-implicit and fully implicit second-order projection methods where the fully implicit method is used in conjunction with a ,smart' time integrator. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Accelerating the coarse time-stepper for a lattice Boltzmann model

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2007
Christophe Vandekerckhove
The equation-free framework for multiscale computing is built around the central idea of a coarse time-stepper, which is an approximate time integrator for the macroscopic variables when only a microscopic simulator is available. In a previous paper, we studied the accuracy and stability of the coarse time-stepper when the microscopic simulator is a lattice Boltzmann model for one-dimensional diffusion. In this paper, we rely on these results to show how the coarse time-stepper can be accelerated using the recently proposed teleprojective method or the multistep state extrapolation method. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

On the practical importance of the SSP property for Runge,Kutta time integrators for some common Godunov-type schemes

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2005
David I. Ketcheson
Abstract We investigate through analysis and computational experiment explicit second and third-order strong-stability preserving (SSP) Runge,Kutta time discretization methods in order to gain perspective on the practical necessity of the SSP property. We consider general theoretical SSP limits for these schemes and present a new optimal third-order low-storage SSP method that is SSP at a CFL number of 0.838. We compare results of practical preservation of the TVD property using SSP and non-SSP time integrators to integrate a class of semi-discrete Godunov-type spatial discretizations. Our examples involve numerical solutions to Burgers' equation and the Euler equations. We observe that ,well-designed' non-SSP and non-optimal SSP schemes with SSP coefficients less than one provide comparable stability when used with time steps below the standard CFL limit. Results using a third-order non-TVD CWENO scheme are also presented. We verify that the documented SSP methods with the number of stages greater than the order provide a useful enhanced stability region. We show by analysis and by numerical experiment that the non-oscillatory third-order reconstructions used in (Liu and Tadmor Numer. Math. 1998; 79:397,425, Kurganov and Petrova Numer. Math. 2001; 88:683,729) are in general only second- and first-order accurate, respectively. Copyright © 2005 John Wiley & Sons, Ltd. [source]