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Explicit Scheme (explicit + scheme)

Distribution by Scientific Domains
Engineering75%
Mathematics and Statistics25%

Selected Abstracts

Explicit integration of bounding surface model for the analysis of earthquake soil liquefaction

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 15 2010
Konstantinos I. Andrianopoulos
Abstract This paper presents a new plasticity model developed for the simulation of monotonic and cyclic loading of non-cohesive soils and its implementation to the commercial finite-difference code FLAC, using its User-Defined-Model (UDM) capability. The new model incorporates the framework of Critical State Soil Mechanics, while it relies upon bounding surface plasticity with a vanished elastic region to simulate the non-linear soil response. Stress integration of constitutive relations is performed using a recently proposed explicit scheme with automatic error control and substepping, which so far has been employed in the literature only for constitutive models aiming at monotonic loading. The overall accuracy of this scheme is evaluated at element level by simulating cyclic loading along complex stress paths and by using iso-error maps for paths involving change of the Lode angle. The performance of the new constitutive model and its stress integration scheme in complex boundary value problems involving earthquake-induced liquefaction is evaluated, in terms of accuracy and computational cost, via a number of parametric analyses inspired by the successful simulation of the VELACS centrifuge Model Test No. 2 studying the lateral spreading response of a liquefied sand layer. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Numerical stability of unsteady stream-function vorticity calculations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 6 2003
E. Sousa
Abstract The stability of a numerical solution of the Navier,Stokes equations is usually approached by con- sidering the numerical stability of a discretized advection,diffusion equation for either a velocity component, or in the case of two-dimensional flow, the vorticity. Stability restrictions for discretized advection,diffusion equations are a very serious constraint, particularly when a mesh is refined in an explicit scheme, so an accurate understanding of the numerical stability of a discretization procedure is often of equal or greater practical importance than concerns with accuracy. The stream-function vorticity formulation provides two equations, one an advection,diffusion equation for vorticity and the other a Poisson equation between the vorticity and the stream-function. These two equations are usually not coupled when considering numerical stability. The relation between the stream-function and the vorticity is linear and so has, in principle, an exact inverse. This allows an algebraic method to link the interior and the boundary vorticity into a single iteration scheme. In this work, we derive a global time-iteration matrix for the combined system. When applied to a model problem, this matrix formulation shows differences between the numerical stability of the full system equations and that of the discretized advection,diffusion equation alone. It also gives an indication of how the wall vorticity discretization affects stability. Despite the added algebraic complexity, it is straightforward to use MATLAB to carry out all the matrix operations. Copyright © 2003 John Wiley & Sons, Ltd. [source]

BILU implicit multiblock Euler/Navier,Stokes simulation for rotor tip vortex and wake convection

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2007
Bowen Zhong
Abstract In this paper, a block incomplete lower,upper (BILU) decomposition method is incorporated with a multiblock three-dimensional Euler/Navier,Stokes solver for simulation of hovering rotor tip vortices and rotor wake convection. Results of both Euler and Navier,Stokes simulations are obtained and compared with experimental observations. The comparisons include surface pressure distributions and tip vortex trajectories. The comparisons suggest that resolution of the boundary layer is important for the accurate evaluation of the blade surface loading, but is less so for the correct prediction of the vortex trajectory. Numerical tests show that, using Courant,Friedrichs,Lewy (CFL) number of 10 or 30 with the developed BILU implicit scheme can be 6,7 times faster than an explicit scheme. The importance of solution acceleration schemes that increase the permitted time-step is illustrated by comparing the evolving wake structures at different stages of the calculation. In contrast to fixed wing simulations, the extent of the wake structures is shown to require resolution of large physical time. This observation explains the poor performance that is obtained when employing convergence acceleration strategies originally intended for solution of equilibrium problems, such as the multigrid methods. Copyright © 2007 John Wiley & Sons, Ltd. [source]

A projection scheme for incompressible multiphase flow using adaptive Eulerian grid

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2004
T. Chen
Abstract This paper presents a finite element method for incompressible multiphase flows with capillary interfaces based on a (formally) second-order projection scheme. The discretization is on a fixed Eulerian grid. The fluid phases are identified and advected using a level set function. The grid is temporarily adapted around the interfaces in order to maintain optimal interpolations accounting for the pressure jump and the discontinuity of the normal velocity derivatives. The least-squares method for computing the curvature is used, combined with piecewise linear approximation to the interface. The time integration is based on a formally second order splitting scheme. The convection substep is integrated over an Eulerian grid using an explicit scheme. The remaining generalized Stokes problem is solved by means of a formally second order pressure-stabilized projection scheme. The pressure boundary condition on the free interface is imposed in a strong form (pointwise) at the pressure-computation substep. This allows capturing significant pressure jumps across the interface without creating spurious instabilities. This method is simple and efficient, as demonstrated by the numerical experiments on a wide range of free-surface problems. Copyright © 2004 John Wiley & Sons, Ltd. [source]

A new parallelization strategy for solving time-dependent 3D Maxwell equations using a high-order accurate compact implicit scheme,

INTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 5 2006
Eugene Kashdan
Abstract With progress in computer technology there has been renewed interest in a time-dependent approach to solving Maxwell equations. The commonly used Yee algorithm (an explicit central difference scheme for approximation of spatial derivatives coupled with the Leapfrog scheme for approximation of temporal derivatives) yields only a second-order of accuracy. On the other hand, an increasing number of industrial applications, especially in optic and microwave technology, demands high-order accurate numerical modelling. The standard way to increase accuracy of the finite difference scheme without increasing the differential stencil is to replace a 2nd-order accurate explicit scheme for approximation of spatial derivatives with the 4th-order accurate compact implicit scheme. In general, such a replacement requires additional memory resources and slows the computations. However, the curl-based form of Maxwell equations allows us to construct an effective parallel algorithm with the alternating domain decomposition (ADD) minimizing the communication time. We present a new parallel approach to the solution of three-dimensional time-dependent Maxwell equations and provide a theoretical and experimental analysis of its performance. Copyright © 2006 John Wiley & Sons, Ltd. [source]

On the finite-differences schemes for the numerical solution of two dimensional Schrödinger equation

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 6 2002
Murat Suba
Abstract In this study three different finite-differences schemes are presented for numerical solution of two-dimensional Schrödinger equation. The finite difference schemes developed for this purpose are based on the (1, 5) fully explicit scheme, and the (5, 5) Noye-Hayman fully implicit technique, and the (3, 3) Peaceman and Rachford alternating direction implicit (ADI) formula. These schemes are second order accurate. The results of numerical experiments are presented, and CPU times needed for this problem are reported. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 752,758, 2002; Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/num.10029. [source]

Lie Theory for Quantum Control

GAMM - MITTEILUNGEN, Issue 1 2008
G. Dirr
Abstract One of the main theoretical challenges in quantum computing is the design of explicit schemes that enable one to effectively factorize a given final unitary operator into a product of basic unitary operators. As this is equivalent to a constructive controllability task on a Lie group of special unitary operators, one faces interesting classes of bilinear optimal control problems for which efficient numerical solution algorithms are sought for. In this paper we give a review on recent Lie-theoretical developments in finite-dimensional quantum control that play a key role for solving such factorization problems on a compact Lie group. After a brief introduction to basic terms and concepts from quantum mechanics, we address the fundamental control theoretic issues for bilinear control systems and survey standard techniques fromLie theory relevant for quantum control. Questions of controllability, accessibility and time optimal control of spin systems are in the center of our interest. Some remarks on computational aspects are included as well. The idea is to enable the potential reader to understand the problems in clear mathematical terms, to assess the current state of the art and get an overview on recent developments in quantum control-an emerging interdisciplinary field between physics, control and computation. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

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]