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General Geometries (general + geometry)

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Selected Abstracts

Stability of a trilinear,trilinear approximation for the Stokes equations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2003
Kamel Nafa
Abstract The choice of mixed finite element approximations for fluid flow problems is a compromise between accuracy and computational efficiency. Although a number of finite elements are found in the literature only few low-order approximations are stable. This is particularly true for three-dimensional flow problems. These elements are attractive because of their simplicity and efficiency, but can suffer though poor rate of convergence. In this paper the stability of a continuous trilinear,trilinear approximation is being analysed for general geometries. Using the macroelement technique, we prove the stability of the approximation. As a result, optimal rates of convergence are obtained for both the velocity and pressure approximations. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Designing materials with prescribed elastic properties using polygonal cells

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2003
Alejandro R. Diaz
Abstract An extension of the material design problem is presented in which the base cell that characterizes the material microgeometry is polygonal. The setting is the familiar inverse homogenization problem as introduced by Sigmund. Using basic concepts in periodic planar tiling it is shown that base cells of very general geometries can be analysed within the standard topology optimization setting with little additional effort. In particular, the periodic homogenization problem defined on polygonal base cells that tile the plane can be replaced and analysed more efficiently by an equivalent problem that uses simple parallelograms as base cells. Different material layouts can be obtained by varying just two parameters that affect the geometry of the parallelogram, namely, the ratio of the lengths of the sides and the internal angle. This is an efficient way to organize the search of the design space for all possible single-scale material arrangements and could result in solutions that may be unreachable using a square or rectangular base cell. Examples illustrate the results. Copyright © 2003 John Wiley & Sons, Ltd. [source]

A stabilized SPH method for inviscid shallow water flows,

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2005
Riadh Ata
Abstract In this paper, the smoothed particle hydrodynamics (SPH) method is applied to the solution of shallow water equations. A brief review of the method in its standard form is first described then a variational formulation using SPH interpolation is discussed. A new technique based on the Riemann solver is introduced to improve the stability of the method. This technique leads to better results. The treatment of solid boundary conditions is discussed but remains an open problem for general geometries. The dam-break problem with a flat bed is used as a benchmark test. Copyright © 2004 John Wiley & Sons, Ltd. [source]

A uniformly stable conformal FDTD-method in Cartesian grids

INTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 2 2003
I.A. Zagorodnov
Abstract A conformal finite-difference time-domain algorithm for the solution of electrodynamic problems in general perfectly conducting 3D geometries is presented. Unlike previous conformal approaches it has the second-order convergence without the need to reduce the maximal stable time step of conventional staircase approach. A novel proof for the local error rate for general geometries is given, and the method is verified and compared to other approaches by means of several numerical 2D examples. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Convergence of MPFA on triangulations and for Richards' equation

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2008
R. A. Klausen
Abstract Spatial discretization of transport and transformation processes in porous media requires techniques that handle general geometry, discontinuous coefficients and are locally mass conservative. Multi-point flux approximation (MPFA) methods are such techniques, and we will here discuss some formulations on triangular grids with further application to the nonlinear Richards equation. The MPFA methods will be rewritten to mixed form to derive stability conditions and error estimates. Several MPFA versions will be shown, and the versions will be discussed with respect to convergence, symmetry and robustness when the grids are rough. It will be shown that the behavior may be quite different for challenging cases of skewness and roughness of the simulation grids. Further, we apply the MPFA discretization approach for the Richards equation and derive new error estimates without extra regularity requirements. The analysis will be accompanied by numerical results for grids that are relevant for practical simulation. Copyright © 2008 John Wiley & Sons, Ltd. [source]