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Several Numerical Experiments (several + numerical_experiment)
Selected AbstractsAn assumed-gradient finite element method for the level set equationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2005Hashem M. Mourad Abstract The level set equation is a non-linear advection equation, and standard finite-element and finite-difference strategies typically employ spatial stabilization techniques to suppress spurious oscillations in the numerical solution. We recast the level set equation in a simpler form by assuming that the level set function remains a signed distance to the front/interface being captured. As with the original level set equation, the use of an extensional velocity helps maintain this signed-distance function. For some interface-evolution problems, this approach reduces the original level set equation to an ordinary differential equation that is almost trivial to solve. Further, we find that sufficient accuracy is available through a standard Galerkin formulation without any stabilization or discontinuity-capturing terms. Several numerical experiments are conducted to assess the ability of the proposed assumed-gradient level set method to capture the correct solution, particularly in the presence of discontinuities in the extensional velocity or level-set gradient. We examine the convergence properties of the method and its performance in problems where the simplified level set equation takes the form of a Hamilton,Jacobi equation with convex/non-convex Hamiltonian. Importantly, discretizations based on structured and unstructured finite-element meshes of bilinear quadrilateral and linear triangular elements are shown to perform equally well. Copyright © 2005 John Wiley & Sons, Ltd. [source] Two-stage computing budget allocation approach for the response surface methodINTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 6 2007J. Peng Abstract Response surface methodology (RSM) is one of the main statistical approaches to search for an input combination that optimizes the simulation output. In the early stages of RSM, an iterative steepest ascent search procedure is frequently used. In this paper, we attempt to improve this procedure by considering a more realistic case where there are computing budget constraints, and formulate a new computing budget allocation problem to look into the important issue of allocating computing budget to the design points in the local region of experimentation. We propose a two-stage computing budget allocation approach, which uses a limited budget to estimate the response surface in the first stage and then uses the rest of the budget to improve the lower bound of the estimated response at the center of the next design region in the second stage. Several numerical experiments are carried out to compare the two-stage approach with the regular factorial design, which allocates budget equally to each design point. The results show that our two-stage allocation outperforms the equal allocation, especially when the system noise is large. [source] Simulation of the Stress-Assisted Densification Behavior of a Powder Compact: Effect of Constitutive LawsJOURNAL OF THE AMERICAN CERAMIC SOCIETY, Issue 3 2008Héctor Camacho-Montes The densification of powders with linear and nonlinear viscous behavior (Scherer and Riedel models) and with power-law-deformation (Khun,McMeeking) behavior was studied under hot pressing and sintering forging conditions. Several numerical experiments, designated cases in this work, were performed to study the effect of (i) the uniaxial stress exerted by the piston and (ii) the rate of the uniaxial stress. The stress state was calculated using the finite-element program ANSYS for each case. Considering the mesoscopic behavior of the powders, densification rates were obtained. The similarities and differences between predictions from the three constitutive models are highlighted. The relationship between the constitutive behavior and the most effective stress state is one of the focuses of this study. For example, we show that under constant stress loading, hot pressing more effectively promotes densification than sinter forging for constitutive behaviors that do not follow the power-law creep. In general, as expected, the increase of uniaxial applied stress and piston velocity favored densification. However, the increase in densification depends strongly on the constitutive law. [source] Conservative constraint for a quasi-uniform overset grid on the sphereTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 616 2006Xindong Peng Abstract A conservative constraint is presented for a new quasi-uniform overset (Yin-Yang) grid on the sphere. The Yin-Yang grid is a newly developed grid system in spherical geometry created by matching two notched latitude,longitude grids which are normal to each other. Global and local conservation is achieved with an interpolation algorithm that exactly guarantees that the fluxes on boundaries of the two grid components are identical. Several numerical experiments are shown to confirm the conservation in passive transport situations and shallow-water dynamical equations. Copyright © 2006 Royal Meteorological Society. [source] An Adaptive Strategy for the Local Discontinuous Galerkin Method Applied to Porous Media ProblemsCOMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 4 2008Esov S. Velázquez DG methods may be viewed as high-order extensions of the classical finite volume method and, since no interelement continuity is imposed, they can be defined on very general meshes, including nonconforming meshes, making these methods suitable for h-adaptivity. The technique starts with an initial conformal spatial discretization of the domain and, in each step, the error of the solution is estimated. The mesh is locally modified according to the error estimate by performing two local operations: refinement and agglomeration. This procedure is repeated until the solution reaches a desired accuracy. The performance of this technique is examined through several numerical experiments and results are compared with globally refined meshes in examples with known analytic solutions. [source] Numerical simulation of bubble and droplet deformation by a level set approach with surface tension in three dimensionsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9 2010Roberto Croce Abstract In this paper we present a three-dimensional Navier,Stokes solver for incompressible two-phase flow problems with surface tension and apply the proposed scheme to the simulation of bubble and droplet deformation. One of the main concerns of this study is the impact of surface tension and its discretization on the overall convergence behavior and conservation properties. Our approach employs a standard finite difference/finite volume discretization on uniform Cartesian staggered grids and uses Chorin's projection approach. The free surface between the two fluid phases is tracked with a level set (LS) technique. Here, the interface conditions are implicitly incorporated into the momentum equations by the continuum surface force method. Surface tension is evaluated using a smoothed delta function and a third-order interpolation. The problem of mass conservation for the two phases is treated by a reinitialization of the LS function employing a regularized signum function and a global fixed point iteration. All convective terms are discretized by a WENO scheme of fifth order. Altogether, our approach exhibits a second-order convergence away from the free surface. The discretization of surface tension requires a smoothing scheme near the free surface, which leads to a first-order convergence in the smoothing region. We discuss the details of the proposed numerical scheme and present the results of several numerical experiments concerning mass conservation, convergence of curvature, and the application of our solver to the simulation of two rising bubble problems, one with small and one with large jumps in material parameters, and the simulation of a droplet deformation due to a shear flow in three space dimensions. Furthermore, we compare our three-dimensional results with those of quasi-two-dimensional and two-dimensional simulations. This comparison clearly shows the need for full three-dimensional simulations of droplet and bubble deformation to capture the correct physical behavior. Copyright © 2009 John Wiley & Sons, Ltd. [source] Parallel coarse-grid selectionNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 8 2007David M. Alber Abstract Algebraic multigrid (AMG) is a powerful linear solver with attractive parallel properties. A parallel AMG method depends on efficient, parallel implementations of the coarse-grid selection algorithms and the restriction and prolongation operator construction algorithms. In the effort to effectively and quickly select the coarse grid, a number of parallel coarsening algorithms have been developed. This paper examines the behaviour of these algorithms in depth by studying the results of several numerical experiments. In addition, new parallel coarse-grid selection algorithms are introduced and tested. Copyright © 2007 John Wiley & Sons, Ltd. [source] | ||||||||||