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Transverse permeability of woven fabrics

INTERNATIONAL JOURNAL OF MATERIAL FORMING 2008年第1期1卷 859-862页

作者： Grouve, W. J. B. Akkerman, R. Loendersloot, R. van den Berg, S. Univ Twente NL-7500 AE Enschede Netherlands Reden Hengelo Netherlands

The transverse permeability is an essential input in describing the consolidation process of CETEX (R) laminates. A two-dimensional, finite difference based, Stokes flow solver has been developed to determine the mesoscopic permeability of arbitrary fabric structures. The use of a multigrid solver dramatically decreases the cpu time required (less than one minute on a 512(2) grid). The permeability of a square packed bed of impenetrable cylinders is calculated and shows excellent agreement with values found in literature.

关键词： Transverse permeability Stokes equation multigrid algorithm

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Discrete adjoint-based approach for optimization problems on three-dimensional unstructured meshes

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AIAA JOURNAL 2007年第4期45卷 740-750页

作者： Mavriplis, Dimitri J. Univ Wyoming Dept Mech Engn Laramie WY 82071 USA

A comprehensive strategy for developing and implementing discrete adjoint methods for aerodynamic shape optimization problems is presented. By linearizing each procedure in the entire optimization problem, transposing each linearization, and reversing the sequential order of operations, the adjoint of the complete optimization problem, including flow equations and mesh motion equations is constructed in a modular and verifiable fashion. This construction is also shown to produce minimal memory overheads and retain the same convergence characteristics of the original analysis problem in the sensitivity analysis. These techniques are implemented in a three-dimensional unstructured multigrid Navier-Stokes solver and demonstrated on a transonic drag reduction problem for a wing body configuration.

关键词： Flow Equations Aerodynamic Shape Optimization Navier Stokes Solver Sensitivity Analysis Wing Body Configuration multigrid algorithm Reynolds Averaged Navier Stokes Lift Coefficient Spalart Allmaras Turbulence Model Stiffness Matrices

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Centered and upwind multigrid turbulent flow simulations of launch vehicle configurations

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JOURNAL OF SPACECRAFT AND ROCKETS 2007年第1期44卷 52-65页

作者： Bigarella, Enda Dimitri Vieira Azevedo, Joao Luiz F. Scalabrin, Leonardo Costa Inst Tecnol Aeronaut Ctr Tecn Aerosp BR-12228900 Sao Jose Dos Campos Brazil Inst Aeronaut & Espaco BR-12228900 Sao Jose Dos Campos Brazil Univ Michigan Dept Aerosp Engn Ann Arbor MI 48109 USA

The paper discusses results obtained with a finite-volume code that simulates viscous, turbulent flows for. 3-D, adaptive, unstructured meshes. The implementation uses a cell-centered, face-based data structure. A fully explicit, second-order accurate, five-stage, Runge-Kutta time stepping scheme is used to perform the time marching of the flow equations.. Spatial discretization of the Reynolds-averaged Navier-Stokes equations can be performed with second-order centered or upwind schemes. Automatic grid refinement routines are considered to adapt the original mesh. A sensor based on density gradients selects the volumes to be refined. The code is able to handle tetrahedra, hexahedra, wedges, and pyramids. A full multigrid scheme is available to accelerate convergence to steady state. Coarse grid levels *** through an agglomeration procedure. One- and two-equation turbulence models are implemented to include the turbulent effects into the numerical formulation. The *** integrated in one single code allow the Brazilian aerospace program to simulate complex flow conditions for sounding rockets and satellite launch vehicles with accuracy and reasonable computational resources. Good agreement with theoretical or experimental results is obtained with the present numerical tool.

关键词： Launch Vehicle Configurations Flow Conditions Reynolds Averaged Navier Stokes Aerodynamic Flow Simulations Eddy Viscosity Turbulence Models multigrid algorithm Euler Equations Sensors Sounding Rockets Angle of Attack

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Higher-order time-integration schemes for aeroelastic applications on unstructured meshes

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AIAA JOURNAL 2007年第1期45卷 138-150页

作者： Yang, Zhi Mavriplis, Dimitri J. Univ Wyoming Dept Engn Mech Laramie WY 82071 USA

Efficient techniques for computational aeroelasticity on unstructured meshes are investigated. These include the formulation of a fourth-order implicit Runge-Kutta time-integration scheme, a third-order backward-difference time-integration scheme, and a second-order backward-difference time-integration scheme for the coupled system of How and structural equations. Strong coupling between the flow solution and structural equations is maintained by fully converging the fully coupled system at each time step or stage. The time-integration schemes are constructed such that discrete conservation is maintained in the flow solution in the presence of dynamically deforming meshes, by verifying the discrete geometric conservation law. Efficient multigrid solution techniques are devised for solving both the governing How equations and the mesh motion equations, using the same agglomerated coarse levels for both problems. The flutter boundary prediction of the AGARD 445.6 wing is used to demonstrate the accuracy and efficiency of these techniques as well as the sensitivity of flutter boundary prediction to time-step size and temporal errors.

关键词： Computational Structural Dynamics CFD Freestream Mach Number Flow Equations Unsteady Flows Arbitrary Lagrangian Eulerian Aeroelasticity multigrid Methods multigrid algorithm Wing Root

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Mesh deformation strategy optimized by the adjoint method on unstructured meshes

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AIAA JOURNAL 2007年第12期45卷 2885-2896页

作者： Yang, Zhi Mavriplis, Dirnitri J. Univ Wyoming Dept Mech Engn Laramie WY 82071 USA

An adjoint-based optimization procedure is proposed for improving the robustness and extending the range of linear-elasticity-based mesh deformation techniques. Using the values of the modulus of elasticity E defined in each mesh cell as the design variables, the procedure seeks to determine an optimum distribution of E throughout the mesh, to minimize a global objective function that reflects the skewness or lack of quality of the deformed mesh. The technique is applied to highly stretched mixed element meshes in two and three dimensions on complex geometries and is shown to be capable of recovering a valid mesh in a small number of optimization cycles for cases in which the nonoptimized linear-elasticity approach fails. However, the solution of the optimization problem remains relatively costly in terms of CPU time, compared with a nonoptimized mesh deformation calculation, making this technique best suited for precomputing improved E distributions before the simulation or for use as a plug-in module to be invoked in cases in which the nonoptimized procedure fails.

关键词： Linear Elasticity Poisson's Ratio Optimization algorithm Stiffness Matrices Steepest Descent Method multigrid algorithm Landing Gear Computing Shape Optimization Trailing Edge Flap

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multigrid Newton-Krylov method for radiation in diffusive semitransparent media

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2007年第2期203卷 498-515页

作者： Seaid, Mohammed Tech Univ Darmstadt Fachbereich Math D-64289 Darmstadt Germany

We present a fast multigrid solver for simplified P-N (SPN) approximations to the diffusive radiation in non-grey semitransparent media. The method consists on reformulating the equations as a nonlinear fixed point problem in the temperature only. Given a mesh hierarchy, time and space discretizations are performed using second-order implicit and finite differencing methods, respectively. At each mesh level, a Newton-Krylov algorithm is applied to the discrete equations. As a smoother on the coarse meshes we propose the Atkinson-Brakhage operator. Numerical results are shown for glass cooling process using different geometry enclosures. The SPN approximations capture the correct asymptotic behavior of the numerical solution with a computational cost lower than using the full radiative transfer equations. (C) 2006 Elsevier B.V. All rights reserved.

关键词： radiative heat transfer SPN approximations Newton-Krylov methods multigrid algorithm glass cooling simulations

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Wavelet filtering for exact controllability of the wave equation

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 2006年第5期28卷 1851-1885页

作者： Negreanu, M. Matache, A. -M. Schwab, C. Univ Complutense Madrid Fac Math Dept Algebra E-28040 Madrid Spain ETH Zentrum Seminar Appl Math CH-8092 Zurich Switzerland

In this paper we propose and analyze a wavelet-based numerical method for exact controllability of the one-dimensional wave equation, concentrating on the particular case of Dirichlet controls. We use the Hilbert uniqueness method (HUM) and prove this result in the context of the finite element space semidiscretization with spline wavelet basis functions. The algorithm for the numerical construction of the controls is based on a conjugate gradient method proposed by Glowinski [J. Comput. Phys., 103 (1992), pp. 189-221] and a two-grid filtering technique in the wavelet basis. We show that wavelet filtering yields numerically exact controllability in the optimal time of the continuous problem and the convergence of the numerical controls using a multilevel discretization filtering technique. Classical arguments then allow proving the uniform boundedness of the numerical controls and passing to the limit as the mesh size tends to zero. We prove that the condition number of the discretized HUM operator. with wavelet filtering is uniformly bounded with respect to the mesh width and prove convergence of the numerical controls obtained with the two-grid filtering technique. Numerical experiments show that wavelet filtering yields numerical controls with the same control time T as in the continuous case.

关键词： boundary controllability uniform observability multigrid algorithm finite element discretization wavelet filtering wave equation

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Preconditioned HLLE method for flows at all Mach numbers

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AIAA JOURNAL 2006年第11期44卷 2645-2653页

作者： Park, Soo Hyung Lee, Jae Eun Kwon, Jang Hyuk Konkuk Univ Seoul 143701 South Korea Korea Adv Inst Sci & Technol Dept Aerosp Engn Taejon 305701 South Korea

A two-dimensional preconditioned multigrid Navier-Stokes solver has been developed for all Mach number viscous flows. For the computation of all Mach number flows, a local preconditioning technique with a modified reference velocity was used to extend the Harten-Lax-van Leer-Einfeldt (HLLE+) scheme, which has good characteristics for compressible viscous flows. The developed methods used to compute several representative steady problems. Grid refinement and parametric studies are performed to verify the performance. The results show that the preconditioned HLLE+ scheme can be successfully applied to a wide variety of flows and that the implicit multigrid solver provides good convergence for the test problems.

关键词： Freestream Mach Number In Compressible Viscous Flows Richardson Extrapolation Rayleigh Numbers Aspect Ratio Shock Capturing Method Switching Mechanisms multigrid algorithm Pressure Coefficient Vortices

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multigrid solution of the discrete adjoint for optimization problems on unstructured meshes

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AIAA JOURNAL 2006年第1期44卷 42-50页

作者： Mavriplis, DJ Univ Wyoming Dept Mech Engn Laramie WY 82071 USA

Techniques for the efficient formulation and solution of file discrete adjoint problem for the Reynolds-averaged Navier-Stokes equations and for the mesh deformation equations are developed for use on unstructured grids in two dimensions. An explicit two-pass approach is used to construct the second-order-accurate flow adjoint equations. and a defect-correction scheme is used to solve the flow adjoint equations, employing a line-implicit agglomeration multigrid strategy to drive the defect-correction scheme. A similar line-implicit multigrid approach is used to solve the mesh deformation equations, as well as the adjoint system of these equations. For the flow sensitivity and mesh motion equations, the multigrid solver is constructed to be duality preserving, delivering similar convergence rates for the primal and dual (adjoint) problems in both cases. These techniques are demonstrated for a viscous turbulent airfoil shape optimization problem.

关键词： NACA 0012 Shape Optimization Unstructured Grid Reynolds Averaged Navier Stokes Flow Equations Freestream Mach Number Lift Coefficient Turbulent Flow Iterative Solution multigrid algorithm

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Variational image reconstruction from arbitrarily spaced samples:: A fast multiresolution spline solution

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IEEE TRANSACTIONS ON IMAGE PROCESSING 2005年第4期14卷 450-460页

作者： Arigovindan, M Sühling, M Hunziker, P Unser, M Ecole Polytech Fed Lausanne Biomed Imaging Grp CH-1015 Lausanne Switzerland Univ Basel Hosp CH-4031 Basel Switzerland

We propose a novel method for image reconstruction from nonuniform samples with no constraints on their locations. We adopt a variational approach where the reconstruction is formulated as the minimizer of a cost that is a weighted sum of two terms: 1) the sum of squared errors at the specified points and 2) a quadratic functional that penalizes the lack of smoothness. We search for a solution that is a uniform spline and show how it can be determined by solving a large, sparse system of linear equations. We interpret the solution of our approach as an approximation of the analytical solution that involves radial basis functions and demonstrate the computational advantages of our approach. Using the two-scale relation for B-splines, we derive an algebraic relation that links together the linear systems of equations specifying reconstructions at different levels of resolution. We use this relation to develop a fast multigrid algorithm. We demonstrate the effectiveness of our approach on some image reconstruction examples.

关键词： B-splines multigrid algorithm multiresolution reconstruction nonuniform interpolation radial basis functions (RBFs) thin-plate splines variational reconstruction

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