2,475 research outputs found
Verification of Unstructured Grid Adaptation Components
Adaptive unstructured grid techniques have made limited impact on production analysis workflows where the control of discretization error is critical to obtaining reliable simulation results. Recent progress has matured a number of independent implementations of flow solvers, error estimation methods, and anisotropic grid adaptation mechanics. Known differences and previously unknown differences in grid adaptation components and their integrated processes are identified here for study. Unstructured grid adaptation tools are verified using analytic functions and the Code Comparison Principle. Three analytic functions with different smoothness properties are adapted to show the impact of smoothness on implementation differences. A scalar advection-diffusion problem with an analytic solution that models a boundary layer is adapted to test individual grid adaptation components. Laminar flow over a delta wing and turbulent flow over an ONERA M6 wing are verified with multiple, independent grid adaptation procedures to show consistent convergence to fine-grid forces and a moment. The scalar problems illustrate known differences in a grid adaptation component implementation and a previously unknown interaction between components. The wing adaptation cases in the current study document a clear improvement to existing grid adaptation procedures. The stage is set for the infusion of verified grid adaptation into production fluid flow simulations
Fourier-based schemes with modified Green operator for computing the electrical response of heterogeneous media with accurate local fields
A modified Green operator is proposed as an improvement of Fourier-based
numerical schemes commonly used for computing the electrical or thermal
response of heterogeneous media. Contrary to other methods, the number of
iterations necessary to achieve convergence tends to a finite value when the
contrast of properties between the phases becomes infinite. Furthermore, it is
shown that the method produces much more accurate local fields inside
highly-conducting and quasi-insulating phases, as well as in the vicinity of
the phases interfaces. These good properties stem from the discretization of
Green's function, which is consistent with the pixel grid while retaining the
local nature of the operator that acts on the polarization field. Finally, a
fast implementation of the "direct scheme" of Moulinec et al. (1994) that
allows for parcimonious memory use is proposed.Comment: v2: `postprint' document (a few remaining typos in the published
version herein corrected in red; results unchanged
Concurrent Multiscale Computing of Deformation Microstructure by Relaxation and Local Enrichment with Application to Single-Crystal Plasticity
This paper is concerned with the effective modeling of deformation microstructures within a concurrent multiscale computing framework. We present a rigorous formulation of concurrent multiscale computing based on relaxation; we establish the connection between concurrent multiscale computing and enhanced-strain elements; and we illustrate the approach in an important area of application, namely, single-crystal plasticity, for which the explicit relaxation of the problem is derived analytically. This example demonstrates the vast effect of microstructure formation on the macroscopic behavior of the sample, e.g., on the force/travel curve of a rigid indentor. Thus, whereas the unrelaxed model results in an overly stiff response, the relaxed model exhibits a proper limit load, as expected. Our numerical examples additionally illustrate that ad hoc element enhancements, e.g., based on polynomial, trigonometric, or similar representations, are unlikely to result in any significant relaxation in general
Preconditioning of weighted H(div)-norm and applications to numerical simulation of highly heterogeneous media
In this paper we propose and analyze a preconditioner for a system arising
from a finite element approximation of second order elliptic problems
describing processes in highly het- erogeneous media. Our approach uses the
technique of multilevel methods and the recently proposed preconditioner based
on additive Schur complement approximation by J. Kraus (see [8]). The main
results are the design and a theoretical and numerical justification of an
iterative method for such problems that is robust with respect to the contrast
of the media, defined as the ratio between the maximum and minimum values of
the coefficient (related to the permeability/conductivity).Comment: 28 page
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