Adaptive Grid (adaptive + grid)

Distribution by Scientific Domains


Selected Abstracts


Adaptive grid based on geometric conservation law level set method for time dependent PDE

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 3 2009
Ali R. Soheili
Abstract A new method for mesh generation is formulated based on the level set functions, which are solutions of the standard level set evolution equation with the Cartesian coordinates as initial values (Liao et al. J Comput Phys 159 (2000), 103,122; Osher and Sethian J Comput Phys 79 (1988), 12; Sethian, Level set methods and fast marching methods, Cambridge University Press, 1999; Di et al. J Sci Comput 31 (2007), 75,98). The intersection of the level contours of the evolving functions form a new grid at each time. The velocity vector in the evolution equation is chosen according to the Geometric Conservation Law (GCL) method (Cao et al., SIAM J Sci Comput 24 (2002), 118,142.). This method has precise control over the Jacobian of transformation because of using the GCL method. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 [source]


A new fast hybrid adaptive grid generation technique for arbitrary two-dimensional domains

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2010
Mohamed S. Ebeida
Abstract This paper describes a new fast hybrid adaptive grid generation technique for arbitrary two-dimensional domains. This technique is based on a Cartesian background grid with square elements and quadtree decomposition. A new algorithm is introduced for the distribution of boundary points based on the curvature of the domain boundaries. The quadtree decomposition is governed either by the distribution of the boundary points or by a size function when a solution-based adaptive grid is desired. The resulting grid is quaddominant and ready for the application of finite element, multi-grid, or line-relaxation methods. All the internal angles in the final grid have a lower bound of 45° and an upper bound of 135°. Although our main interest is in grid generation for unsteady flow simulations, the technique presented in this paper can be employed in many other fields. Several application examples are provided to illustrate the main features of this new approach. Copyright © 2010 John Wiley & Sons, Ltd. [source]


Handling constraints using multiobjective optimization concepts

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2004
Arturo Hernández Aguirre
Abstract In this paper, we propose a new constraint-handling technique for evolutionary algorithms which we call inverted-shrinkable PAES (IS-PAES). This approach combines the use of multiobjective optimization concepts with a mechanism that focuses the search effort onto specific areas of the feasible region by shrinking the constrained search space. IS-PAES also uses an adaptive grid to store the solutions found, but has a more efficient memory-management scheme than its ancestor (the Pareto archived evolution strategy for multiobjective optimization). The proposed approach is validated using several examples taken from the standard evolutionary and engineering optimization literature. Comparisons are provided with respect to the stochastic ranking method (one of the most competitive constraint-handling approaches used with evolutionary algorithms currently available) and with respect to other four multiobjective-based constraint-handling techniques. Copyright© 2004 John Wiley & Sons, Ltd. [source]


Experimental validation of a rigorous absorber model for CO2 postcombustion capture

AICHE JOURNAL, Issue 4 2007
Finn Andrew Tobiesen
Abstract A rigorous rate-based model for acid gas absorption was developed and validated against mass-transfer data obtained from a 3-month campaign in a laboratory pilot-plant absorber in which the experimental gas,liquid material balance was within an average of 6%. The mass-transfer model is based on the penetration theory where the liquid film is discretized using an adaptive grid. The model was validated against all data and the deviation between simulated and averaged gas and liquid side experimental mass-transfer rates yielded a total variability of 6.26%, while the total average deviation was 6.16%. Simpler enhancement factor mass-transfer models were also tested, but showed slight over-prediction of mass-transfer rates. A sensitivity analysis shows that the accuracy of the equilibrium model is the single most important source of deviation between experiments and model, in particular at high loadings. Experimental data for the absorber in the integrated pilot plant are included. © 2007 American Institute of Chemical Engineers AIChE J, 2007 [source]


Simulations of strong gravitational lensing with substructure

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 4 2006
Adam Amara
ABSTRACT Galactic-sized gravitational lenses are simulated by combining a cosmological N -body simulation and models for the baryonic component of the galaxy. The lens caustics, critical curves, image locations and magnification ratios are calculated by ray shooting on an adaptive grid. When the source is near a cusp in a smooth lens' caustic, the sum of the magnifications of the three closest images should be close to zero. It is found that in the observed cases this sum is generally too large to be consistent with the simulations, implying that there is not enough substructure in the simulations. This suggests that other factors play an important role. These may include limited numerical resolution, lensing by structure outside the halo, selection bias and the possibility that a randomly selected galaxy halo may be more irregular, for example, due to recent mergers, than the isolated halo used in this study. It is also shown that, with the level of substructure computed from the N -body simulations, the image magnifications of the Einstein cross-type lenses are very weak functions of source size up to 1 kpc. This is also true for the magnification ratios of widely separated images in the fold and cusp,caustic lenses. This means that selected magnification ratios for the different emission regions of a lensed quasar should agree with each other, barring microlensing by stars. The source size dependence of the magnification ratio between the closest pair of images is more sensitive to substructure. [source]


Quantum wave packet dynamics on multidimensional adaptive grids: Applications of the moving boundary truncation method

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 7 2007
Lucas R. Pettey
Abstract Recently, we reported a novel method for integrating the time dependent Schrödinger equation which used hydrodynamic quantum trajectories to adapt the boundaries of a fixed spatial grid. The moving boundary truncation (MBT) method significantly reduced the number of grid points needed to perform accurate calculations while maintaining stability during the time propagation. In this work, the method is extended to multidimensional examples. The application of MBT to scattering on 2D and 3D potential energy surfaces shows a greater decrease in the number of grid points needed compared with full fixed grids while maintaining excellent accuracy and stability, even for very long propagation times. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007 [source]


The effect of overall discretization scheme on Jacobian structure, convergence rate, and solution accuracy within the local rectangular refinement method

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 8 2001
Beth Anne V. Bennett
Abstract The local rectangular refinement (LRR) solution-adaptive gridding method automatically produces orthogonal unstructured adaptive grids and incorporates multiple-scale finite differences to discretize systems of elliptic governing partial differential equations (PDEs). The coupled non-linear discretized equations are solved simultaneously via Newton's method with a Bi-CGSTAB linear system solver. The grids' unstructured nature produces a nonstandard sparsity pattern within the Jacobian. The effects of two discretization schemes (LRR multiple-scale stencils and traditional single-scale stencils) on Jacobian bandwidth, convergence speed, and solution accuracy are studied. With various point orderings, for two simple problems with analytical solutions, the LRR multiple-scale stencils are seen to: (1) produce Jacobians of smaller bandwidths than those resulting from the traditional single-scale stencils; (2) lead to significantly faster Newton's method convergence than the single-scale stencils; and (3) produce more accurate solutions than the single-scale stencils. The LRR method, including the LRR multiple-scale stencils, is finally applied to an engineering problem governed by strongly coupled, highly non-linear PDEs: a steady-state lean Bunsen flame with complex chemistry, multicomponent transport, and radiation modeling. Very good agreement is observed between the computed flame height and previously published experimental data. Copyright © 2001 John Wiley & Sons, Ltd. [source]