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Uniform Grids (uniform + grid)
Selected AbstractsMeasurement of the spatial distribution of fluvial bedload transport velocity in both sand and gravelEARTH SURFACE PROCESSES AND LANDFORMS, Issue 10 2004Colin D. Rennie Abstract Maps are presented of the spatial distribution of two-dimensional bedload transport velocity vectors. Bedload velocity data were collected using the bottom tracking feature of an acoustic Doppler current pro,ler (aDcp) in both a gravel-bed reach and a sand-bed reach of Fraser River, British Columbia. Block-averaged bedload velocity vectors, and bedload velocity vectors interpolated onto a uniform grid, revealed coherent patterns in the bedload velocity distribution. Concurrent Helley-Smith bedload sampling in the sand-bed reach corroborated the trends observed in the bedload velocity map. Contemporaneous 2D vector maps of near-bed water velocity (velocity in bins centered between 25 cm and 50 cm from the bottom) and depth-averaged water velocity were also generated from the aDcp data. Using a vector correlation coef,cient, which is independent of the choice of coordinate system, the bedload velocity distribution was signi,cantly correlated to the near-bed and depth-averaged water velocity distributions. The bedload velocity distribution also compared favorably with variations in depth and estimates of the spatial distribution of shear stress. Published in 2004 by John Wiley & Sons, Ltd. [source] On accuracy of the finite-difference and finite-element schemes with respect to P -wave to S -wave speed ratioGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2010Peter Moczo SUMMARY Numerical modelling of seismic motion in sedimentary basins often has to account for P -wave to S -wave speed ratios as large as five and even larger, mainly in sediments below groundwater level. Therefore, we analyse seven schemes for their behaviour with a varying P -wave to S -wave speed ratio. Four finite-difference (FD) schemes include (1) displacement conventional-grid, (2) displacement-stress partly-staggered-grid, (3) displacement-stress staggered-grid and (4) velocity,stress staggered-grid schemes. Three displacement finite-element schemes differ in integration: (1) Lobatto four-point, (2) Gauss four-point and (3) Gauss one-point. To compare schemes at the most fundamental level, and identify basic aspects responsible for their behaviours with the varying speed ratio, we analyse 2-D second-order schemes assuming an elastic homogeneous isotropic medium and a uniform grid. We compare structures of the schemes and applied FD approximations. We define (full) local errors in amplitude and polarization in one time step, and normalize them for a unit time. We present results of extensive numerical calculations for wide ranges of values of the speed ratio and a spatial sampling ratio, and the entire range of directions of propagation with respect to the spatial grid. The application of some schemes to real sedimentary basins in general requires considerably finer spatial sampling than usually applied. Consistency in approximating first spatial derivatives appears to be the key factor for the behaviour of a scheme with respect to the P -wave to S -wave speed ratio. [source] Study on flow past two spheres in tandem arrangement using a local mesh refinement virtual boundary methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2005Jian-Feng Zou Abstract A local mesh refinement virtual boundary method based on a uniform grid is designed to study the transition between the flow patterns of two spheres in tandem arrangement for Re=250. For a small gap (L/D=1.5), the flow field is axisymmetric. As the spacing ratio increases to 2.0, the pressure gradient induces the circumferential fluid motion and a plane-symmetric flow is constructed through a regular bifurcation. For L/D,2.5, the vortices are periodically shed from the right sphere, but the planar symmetry remains. The case for L/D=3.0 is picked up to give a detail investigation for the unsteady flow. The shedding frequency of vortical structure from the upper side of the right sphere is found to be double of the frequency of the lower side. With the flow spectra of various gaps given, the underlying competitive mechanism between the two shedding frequencies is studied and a critical spacing gap is revealed. Copyright © 2005 John Wiley & Sons, Ltd. [source] A comparative study on interpolation methods for controlled cardiac CTINTERNATIONAL JOURNAL OF IMAGING SYSTEMS AND TECHNOLOGY, Issue 2 2007Deepak Bharkhada Abstract Bai et al. recently proposed to acquire random fan-beam/cone-beam projections with a linear/planar detector from a circular scanning locus for controlled cardiac computed tomography (CT). After specifying a uniform acquisition geometry required by FBP (filtration-backprojection), we rebin the random fan-beam/cone-beam data via nearest-neighbor, quadrilateral and triangle-based linear interpolation methods. The fan-beam and parallel-beam FBP algorithms are employed for rebinned fan-beam projections. The FDK (Feldkamp,Davis,Kress) and t-FDK (tent-FDK) methods are employed for rebinned cone-beam data. Also, nonuniform weighting fan-beam/FDK methods are used to reconstruct without rebinning. As a benchmark, the images are reconstructed using uniform weighting fan-beam/FDK method from data collected at the specified uniform grid. To evaluate the different methods, effects of increasing the number of projections and adding Poisson noise are studied. The root mean square error (RMSE) is used to quantify the image quality by numerical tests with the cardiac phantom. Our results show that it is helpful to perform data interpolation for improvements of the image quality in controlled cardiac CT from random projections. Our simulations indicate that triangular interpolation gives the most satisfactory result for improved image quality whereas quadrilateral interpolationgives the best noise performance. © 2007 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 17, 91,98, 2007 [source] Polygonal finite elements for topology optimization: A unifying paradigmINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2010Cameron Talischi Abstract In topology optimization literature, the parameterization of design is commonly carried out on uniform grids consisting of Lagrangian-type finite elements (e.g. linear quads). These formulations, however, suffer from numerical anomalies such as checkerboard patterns and one-node connections, which has prompted extensive research on these topics. A problem less often noted is that the constrained geometry of these discretizations can cause bias in the orientation of members, leading to mesh-dependent sub-optimal designs. Thus, to address the geometric features of the spatial discretization, we examine the use of unstructured meshes in reducing the influence of mesh geometry on topology optimization solutions. More specifically, we consider polygonal meshes constructed from Voronoi tessellations, which in addition to possessing higher degree of geometric isotropy, allow for greater flexibility in discretizing complex domains without suffering from numerical instabilities. Copyright © 2009 John Wiley & Sons, Ltd. [source] Surface wavelets: a multiresolution signal processing tool for 3D computational modellingINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2001Kevin Amaratunga Abstract In this paper, we provide an introduction to wavelet representations for complex surfaces (surface wavelets), with the goal of demonstrating their potential for 3D scientific and engineering computing applications. Surface wavelets were originally developed for representing geometric objects in a multiresolution format in computer graphics. These wavelets share all of the major advantages of conventional wavelets, in that they provide an analysis tool for studying data, functions and operators at different scales. However, unlike conventional wavelets, which are restricted to uniform grids, surface wavelets have the power to perform signal processing operations on complex meshes, such as those encountered in finite element modelling. This motivates the study of surface wavelets as an efficient representation for the modelling and simulation of physical processes. We show how surface wavelets can be applied to partial differential equations, stated either in integral form or in differential form. We analyse and implement the wavelet approach for a model 3D potential problem using a surface wavelet basis with linear interpolating properties. We show both theoretically and experimentally that an O(h) convergence rate, hn being the mesh size, can be obtained by retaining only O((logN) 7/2N) entries in the discrete operator matrix, where N is the number of unknowns. The principles described here may also be extended to volumetric discretizations. Copyright © 2001 John Wiley & Sons, Ltd. [source] Stable high-order finite-difference methods based on non-uniform grid point distributionsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2008Miguel Hermanns Abstract It is well known that high-order finite-difference methods may become unstable due to the presence of boundaries and the imposition of boundary conditions. For uniform grids, Gustafsson, Kreiss, and Sundström theory and the summation-by-parts method provide sufficient conditions for stability. For non-uniform grids, clustering of nodes close to the boundaries improves the stability of the resulting finite-difference operator. Several heuristic explanations exist for the goodness of the clustering, and attempts have been made to link it to the Runge phenomenon present in polynomial interpolations of high degree. By following the philosophy behind the Chebyshev polynomials, a non-uniform grid for piecewise polynomial interpolations of degree q,N is introduced in this paper, where N + 1 is the total number of grid nodes. It is shown that when q=N, this polynomial interpolation coincides with the Chebyshev interpolation, and the resulting finite-difference schemes are equivalent to Chebyshev collocation methods. Finally, test cases are run showing how stability and correct transient behaviours are achieved for any degree q Acoustic upwinding for sub- and super-sonic turbulent channel flow at low Reynolds numberINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2007H. C. de LangeArticle first published online: 13 FEB 200 Abstract A recently developed asymmetric implicit fifth-order scheme with acoustic upwinding for the spatial discretization for the characteristic waves is applied to the fully compressible, viscous and non-stationary Navier,Stokes equations for sub- and super-sonic, mildly turbulent, channel flow (Re,=360). For a Mach number of 0.1, results are presented for uniform (323, 643 and 1283) and non-uniform (expanding wall-normal, 323 and 643) grids and compared to the (incompressible) reference solution found in (J. Fluid. Mech. 1987; 177:133,166). The results for uniform grids on 1283 and 643 nodes show high resemblance with the reference solution. Expanding grids are applied on 643 - and 323 -node grids. The capability of the proposed technique to solve compressible flow is first demonstrated by increasing the Mach number to 0.3, 0.6 and 0.9 for isentropic flow on the uniform 643 -grid. Next, the flow speed is increased to Ma=2. The results for the isothermal-wall supersonic flows give very good agreement with known literature results. The velocity field, the temperature and their fluctuations are well resolved. This means that in all presented (sub- and super-sonic) cases, the combination of acoustic upwinding and the asymmetric high-order scheme provides sufficient high wave-number damping and low wave-number accuracy to give numerically stable and accurate results. Copyright © 2007 John Wiley & Sons, Ltd. [source] Cubic-spline interpolation on a non-uniform latitude,longitude grid: achieving cross- and circum-polar continuityATMOSPHERIC SCIENCE LETTERS, Issue 3 2010Markus Gross Abstract Although it is straightforward to construct cubic splines in Cartesian geometry, this is not so for latitude-longitude grids over the sphere, because of the polar singularity. Previous work has either introduced ad hoc approximations over the polar caps, to the detriment of both continuity and accuracy, or has been restricted to interpolation of fields defined on uniform grids, with an even number of meridians, and with known polar values. These limitations are addressed herein by reformulating the construction of bicubic splines as the minimisation of an appropriate integral subject to certain constraints. © Crown Copyright 2010. Reproduced with the permission of HMSO. Published by John Wiley & Sons, Ltd. [source]
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