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Euler Scheme (euler + scheme)

Distribution by Scientific Domains

Mathematics and Statistics	60%
Engineering	40%

Selected Abstracts

An augmented Lagrange multiplier approach to continuum multislip single crystal thermo,elasto,viscoplasticity

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2005
C. C. Celigoj
Abstract The material and structural behaviour of single crystals is going to be investigated. On the constitutive level the concept of ,generalized standard materials (gsm)' is used to set up the equations for finite deformation multislip single crystal thermo,elasto,viscoplasticity within a continuum slip theory. The only two scalar quantities needed are a thermodynamic potential and a dissipation potential. The resulting evolution equations for the internal (viscoplastic) variables are discretized in time and solved via a backward Euler scheme, using an ,augmented Lagrange multiplier method' for satisfying the multiple constraints, thus circumventing the cumbersome and less robust ,active set strategies'. As a computational reference frame serves the Eulerian setting. The structural behaviour (non-linear coupled thermomechanics) is solved in a staggered algorithm: in an isothermal mechanical phase via q1(displacements)/p0(pressure)/j0(jacobian)-finite elements and in an isogeometric thermal phase via q1(temperatures)-finite elements, followed by an isogeometric and isothermal update phase of the internal variables. Numerical results of the simple isothermal shear test of a single face-centred cubic (fcc) crystal and of the thermomechanical behaviour of a geometrically imperfect strip consisting of initially equally oriented (0/45/30 in Euler angles) fcc-crystals under tension and plane strain conditions are given. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Baroclinic stability for a family of two-level, semi-implicit numerical methods for the 3D shallow water equations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2007
Francisco J. Rueda
Abstract The baroclinic stability of a family of two time-level, semi-implicit schemes for the 3D hydrostatic, Boussinesq Navier,Stokes equations (i.e. the shallow water equations), which originate from the TRIM model of Casulli and Cheng (Int. J. Numer. Methods Fluids 1992; 15:629,648), is examined in a simple 2D horizontal,vertical domain. It is demonstrated that existing mass-conservative low-dissipation semi-implicit methods, which are unconditionally stable in the inviscid limit for barotropic flows, are unstable in the same limit for baroclinic flows. Such methods can be made baroclinically stable when the integrated continuity equation is discretized with a barotropically dissipative backwards Euler scheme. A general family of two-step predictor-corrector schemes is proposed that have better theoretical characteristics than existing single-step schemes. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Stability and convergence of optimum spectral non-linear Galerkin methods

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 5 2001
He Yinnian
Abstract Our objective in this article is to present some numerical schemes for the approximation of the 2-D Navier,Stokes equations with periodic boundary conditions, and to study the stability and convergence of the schemes. Spatial discretization can be performed by either the spectral Galerkin method or the optimum spectral non-linear Galerkin method; time discretization is done by the Euler scheme and a two-step scheme. Our results show that under the same convergence rate the optimum spectral non-linear Galerkin method is superior to the usual Galerkin methods. Finally, numerical example is provided and supports our results. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Uniform stability of spectral nonlinear Galerkin methods

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 5 2004
Yinnian He
Abstract This article provides a stability analysis for the backward Euler schemes of time discretization applied to the spatially discrete spectral standard and nonlinear Galerkin approximations of the nonstationary Navier-Stokes equations with some appropriate assumption of the data (,, u0, f). If the backward Euler scheme with the semi-implicit nonlinear terms is used, the spectral standard and nonlinear Galerkin methods are uniform stable under the time step constraint ,t , (2/,,1). Moreover, if the backward Euler scheme with the explicit nonlinear terms is used, the spectral standard and nonlinear Galerkin methods are uniform stable under the time step constraints ,t = O(,) and ,t = O(,), respectively, where , , ,, which shows that the restriction on the time step of the spectral nonlinear Galerkin method is less than that of the spectral standard Galerkin method. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004 [source]