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Triangular Grids (triangular + grid)
Selected AbstractsNumerical simulation of viscous flow interaction with an elastic membraneINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2008Lisa A. Matthews Abstract A numerical fluid,structure interaction model is developed for the analysis of viscous flow over elastic membrane structures. The Navier,Stokes equations are discretized on a moving body-fitted unstructured triangular grid using the finite volume method, taking into account grid non-orthogonality, and implementing the SIMPLE algorithm for pressure solution, power law implicit differencing and Rhie,Chow explicit mass flux interpolations. The membrane is discretized as a set of links that coincide with a subset of the fluid mesh edges. A new model is introduced to distribute local and global elastic effects to aid stability of the structure model and damping effects are also included. A pseudo-structural approach using a balance of mesh edge spring tensions and cell internal pressures controls the motion of fluid mesh nodes based on the displacements of the membrane. Following initial validation, the model is applied to the case of a two-dimensional membrane pinned at both ends at an angle of attack of 4° to the oncoming flow, at a Reynolds number based on the chord length of 4 × 103. A series of tests on membranes of different elastic stiffness investigates their unsteady movements over time. The membranes of higher elastic stiffness adopt a stable equilibrium shape, while the membrane of lowest elastic stiffness demonstrates unstable interactions between its inflated shape and the resulting unsteady wake. These unstable effects are shown to be significantly magnified by the flexible nature of the membrane compared with a rigid surface of the same average shape. Copyright © 2007 John Wiley & Sons, Ltd. [source] Time domain global modelling of EM propagation in semiconductor using irregular gridsINTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 4 2002Hsiao-Ping Tsai Abstract A two-dimensional finite volume time domain (FVTD) method using a triangular grid is applied to the analysis of electromagnetic wave propagation in a semiconductor. Maxwell's equations form the basis of all electromagnetic phenomena in semiconductors and the drift-diffusion model is employed to simulate charge transport phenomena in the semiconductor. The FVTD technique is employed to solve Maxwell's equations on an irregular grid and the finite box method is implemented on the same grid to solve the drift-diffusion model for carrier concentration. The locations of unknowns have been chosen to allow linking coupled Maxwell's equations and transport equations in a seamless way. To achieve suitable accuracy and computational efficiency, using irregular grid topology allows a finer mesh in doped region and at junction, and a coarser mesh in substrate and insulting regions. The proposed scheme has been implemented and verified by characterizing electromagnetic wave propagation at microwave frequency in a semiconductor slab with arbitrary doping profile. Copyright © 2002 John Wiley & Sons, Ltd. [source] On a quadrature algorithm for the piecewise linear wavelet collocation applied to boundary integral equationsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 11 2003Andreas Rathsfeld Abstract In this paper, we consider a piecewise linear collocation method for the solution of a pseudo-differential equation of order r=0, ,1 over a closed and smooth boundary manifold. The trial space is the space of all continuous and piecewise linear functions defined over a uniform triangular grid and the collocation points are the grid points. For the wavelet basis in the trial space we choose the three-point hierarchical basis together with a slight modification near the boundary points of the global patches of parametrization. We choose linear combinations of Dirac delta functionals as wavelet basis in the space of test functionals. For the corresponding wavelet algorithm, we show that the parametrization can be approximated by low-order piecewise polynomial interpolation and that the integrals in the stiffness matrix can be computed by quadrature, where the quadrature rules are composite rules of simple low-order quadratures. The whole algorithm for the assembling of the matrix requires no more than O(N [logN]3) arithmetic operations, and the error of the collocation approximation, including the compression, the approximative parametrization, and the quadratures, is less than O(N,(2,r)/2). Note that, in contrast to well-known algorithms by Petersdorff, Schwab, and Schneider, only a finite degree of smoothness is required. In contrast to an algorithm of Ehrich and Rathsfeld, no multiplicative splitting of the kernel function is required. Beside the usual mapping properties of the integral operator in low order Sobolev spaces, estimates of Calderón,Zygmund type are the only assumptions on the kernel function. Copyright © 2003 John Wiley & Sons, Ltd. [source] Convergence of MPFA on triangulations and for Richards' equationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2008R. 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] Retracted and replaced: A flow-condition-based interpolation finite element procedure for triangular gridsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2005Haruhiko Kohno Abstract A flow-condition-based interpolation finite element scheme is presented for use of triangular grids in the solution of the incompressible Navier,Stokes equations. The method provides spatially isotropic discretizations for low and high Reynolds number flows. Various example solutions are given to illustrate the capabilities of the procedure. This article and been retracted and replaced. See retraction and replacement notice DOI: 10.1002/fld.1247.abs. Copyright © 2005 John Wiley & Sons, Ltd. [source] Numerical simulation of a permittivity probe for measuring the electric properties of planetary regolith and application to the near-surface region of asteroids and cometsMETEORITICS & PLANETARY SCIENCE, Issue 6 2008Klaus SPITZER Our simulation techniques aim at accompanying hardware development and conducting virtual experiments, e.g., to assess the response of arbitrary heterogeneous conductivity and permittivity distributions or to scrutinize possibilities for spatial reconstruction methods using inverse schemes. In a first step, we have developed a finite element simulation code on the basis of unstructured, adaptive triangular grids for arbitrary two-dimensional axisymmetric distributions of conductivity and permittivity. The code is able to take into account the spatial geometry of the probe and allows for possible inductive effects. In previous studies, the non-inductive approach has been used to convert potential and phase data into apparent material properties. By our simulations, we have shown that this approach is valid for the frequency range from 102 Hz to 107 Hz and electric conductivities of 10,8 S/m that are typical for the near-surface region of asteroids and comets composed of chondritic materials and/or frozen volatiles such as H2O and CO2 ice. We prove the accuracy of our code to be better than 10%, using mixed types of boundary conditions and present a simulated vertical log through a horizontally stratified subsurface layer as a representative example of a heterogeneous distribution of the electrical properties. Resolution studies for the given electrode separation reveal that the material parameters of layers having thicknesses of less than about half the electrode spread are not reconstructible if only apparent quantities are considered. Therefore, spatial distributions of the complex sensitivity are presented having in mind a future data inversion concept that will permit the multi-dimensional reconstruction of material parameters in heterogeneous environments. [source] Anisotropic mesh adaptation for numerical solution of boundary value problemsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 4 2004Vít Dolej Abstract We present an efficient mesh adaptation algorithm that can be successfully applied to numerical solutions of a wide range of 2D problems of physics and engineering described by partial differential equations. We are interested in the numerical solution of a general boundary value problem discretized on triangular grids. We formulate a necessary condition for properties of the triangulation on which the discretization error is below the prescribed tolerance and control this necessary condition by the interpolation error. For a sufficiently smooth function, we recall the strategy how to construct the mesh on which the interpolation error is below the prescribed tolerance. Solving the boundary value problem we apply this strategy to the smoothed approximate solution. The novelty of the method lies in the smoothing procedure that, followed by the anisotropic mesh adaptation (AMA) algorithm, leads to the significant improvement of numerical results. We apply AMA to the numerical solution of an elliptic equation where the exact solution is known and demonstrate practical aspects of the adaptation procedure: how to control the ratio between the longest and the shortest edge of the triangulation and how to control the transition of the coarsest part of the mesh to the finest one if the two length scales of all the triangles are clearly different. An example of the use of AMA for the physically relevant numerical simulation of a geometrically challenging industrial problem (inviscid transonic flow around NACA0012 profile) is presented. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004. [source] | |||||||||||||