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Efficient Solution Methods for Strand Grid Applications

AIAA JOURNAL 2014年第2期52卷 267-280页

作者： Katz, Aaron Wissink, Andrew M. Utah State Univ Logan UT 84322 USA NASA Ames Res Ctr US Army Aeroflightdynam Directorate Moffett Field CA 94035 USA

The strand-Cartesian grid approach offers many advantages in terms of automation, efficiency, and accuracy for complex moving-body problems, such as rotorcraft. In this study, the solution procedures for strand grids are investigated by testing a variety of explicit, implicit, and hybrid methods on canonical aerodynamics test cases involving inviscid and viscous flows in three dimensions. A novel multigrid algorithm is formulated that acts at both the nonlinear pseudotime level and the linear level using line Gauss-Seidel sweeps. Various approximations are tested for the Jacobian, and the impacts on memory and convergence are quantified. The major result is that implicit schemes with first-order approximate Jacobians employing few Gauss-Seidel sweeps are most efficient for strand grids. The improvement by using the multigrid algorithm is significant for all cases tested and indicates O(n) convergence.

关键词： multigrid algorithm Freestream Conditions Flow Conditions Rotorcrafts High Aspect Ratio Explicit Methods NACA 0012 Primitive Variable Angle of Attack Laminar Boundary Layer

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Efficient Solvers of Discontinuous Galerkin Discretization for the Cahn-Hilliard Equations

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JOURNAL OF SCIENTIFIC COMPUTING 2014年第2期58卷 380-408页

作者： Guo, Ruihan Xu, Yan Univ Sci & Technol China Sch Math Sci Hefei 230026 Anhui Peoples R China

In this paper, we develop and analyze a fast solver for the system of algebraic equations arising from the local discontinuous Galerkin (LDG) discretization and implicit time marching methods to the Cahn-Hilliard (CH) equations with constant and degenerate mobility. Explicit time marching methods for the CH equation will require severe time step restriction , so implicit methods are used to remove time step restriction. Implicit methods will result in large system of algebraic equations and a fast solver is essential. The multigrid (MG) method is used to solve the algebraic equations efficiently. The Local Mode Analysis method is used to analyze the convergence behavior of the linear MG method. The discrete energy stability for the CH equations with a special homogeneous free energy density is proved based on the convex splitting method. We show that the number of iterations is independent of the problem size. Numerical results for one-dimensional, two-dimensional and three-dimensional cases are given to illustrate the efficiency of the methods. We numerically show the optimal complexity of the MG solver for element. For approximation, the optimal or sub-optimal complexity of the MG solver are numerically shown.

关键词： Cahn-Hilliard equation Local discontinuous Galerkin method Convex splitting method multigrid algorithm FAS multigrid Additive Runge-Kutta Diagonally implicit Runge-Kutta Local mode analysis

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NUMERICAL STUDY OF FLOW AND HEAT TRANSFER IN ROTATING MICROCHANNELS

NUMERICAL STUDY OF FLOW AND HEAT TRANSFER IN ROTATING MICROC...

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作者： PRATANU ROY Texas A&M University

学位级别：博士

Investigation of fluid flow and heat transfer in rotating microchannels is impor- tant for centrifugal microfluidics, which has emerged as an advanced technique in biomedical applications and chemical separations. The centrifugal force and the Coriolis force, arising as a consequence of the microchannel rotation, change the flow pattern significantly from the symmetric profile of a non-rotating channel. A suc- cessful design of a centrifugal microfluidic device depends on effectively regulating these forces in rotating microchannels. Although a large number of experimental studies have been performed in order to demonstrate the applications of centrifugal microfluidics in various fields, a systematic study on the effect of rotation, chan- nel aspect ratio, and wall boundary conditions on the fluid flow and heat transfer phenomena in rotating microchannels has not yet been conducted. During the present study, pressure-based finite volume solvers in both staggered and collocated grids were developed to solve steady and unsteady, incompressible Navier-Stokes equations. The serial solver in collocated grid was parallelized using a Message Passing Interface (MPI) library. In order to accelerate the convergence of the collocated finite volume solver, a non-linear multi-grid method was developed. The parallel performances of the single and multi-grid solvers were tested on a two- dimensional lid driven cavity flow. High fidelity benchmark solution to a lid driven cavity flow problem in a 1024 × 1024 grid was presented for a range of Reynolds num- bers. Parallel multigrid speedup as high as three orders of magnitude was achieved for low Reynolds number flows. In addition, the optimal multigrid efficiency was validated. The fluid flow in a rotating microchannel was modeled as a steady, laminar in- compressible flow with no slip and slip boundary conditions. For no slip boundary condition, critical values of parameters that determine the extent of the centrifugal force and th

关键词： Rotating Microchannels Finite Volume Method multigrid algorithm Parallel algorithm Collocated Grid Slip Boundary Condition Level Set Method Thesis

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Further developments in the multiblock hybrid CFD solver elsA-H 50

Further developments in the multiblock hybrid CFD solver els...

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50th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

作者： De La Llave Plata, Marta Couaillier, Vincent Marmignon, Claude Le Pape, Marie-Claire Gazaix, Michel Cantaloube, Bernard ONERA CFD and Aeroacoustics Department French Aerospace Lab. FR-92322 Châtillon France

ISBN: (数字)9781600869365

Over the past few years, ONERA has been working on the extension of the multiblock structured solver elsA to hybrid-grid configurations. By hybrid grids, we mean those in which structured (ijk-based) and unstructured blocks coexist within the same computational domain. We have called the new solver elsA-H. This approach has a number of advantages which are highlighted in this work. In this paper, we review the hybrid-grid algorithms upon which elsA-H relies, focusing on the particular handling of matching-grid interfaces. We also report recent progress on the parallelisation of such algorithms, as well as on the development of an appropriate hybrid-grid load-balancing tool. Finally, we present preliminary work on the implementation of a hybrid multigrid algorithm into elsA-H. A number of simulation results for several unstructured and hybrid-grid configurations are reported in this paper. Copyright © 2012 by ONERA.

关键词： multigrid algorithm Reynolds Averaged Navier Stokes Unstructured Grid Unsteady Turbulent Flow Detached Eddy Simulation Primitive Variable Aerodynamics Newtonian Fluid Static Pressure NACA 0012

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Study on a Real-time Corner Detection algorithm

Study on a Real-time Corner Detection Algorithm

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International Conference on Micro Nano Devices, Structure and Computing Systems

作者： Guo Yongfang Yu Ming Sun Yicai Hebei Univ Technol Tianjin Peoples R China

ISBN: (纸本)9783037850091

Conventional Harris corner detector is a desirable detector but it requires significantly more computation time. For MIC detector proposed by Trajkovic, the minimal computational demands of its operator make it well-suited for real-time applications, however the Trajkovic's operator responses too readily to certain diagonal edges. For this reason, the paper proposed a new corner detection algorithm. The new corner detection algorithm adopted multigrid algorithm and preprocessed the lower resolution revision of the original image to obtain the potential corners, subsequently used autocorrelation matrix to get the corner response function for the corresponding points of the potential corner. The test results indicate the new corner detection algorithm can decrease edge responses and the number of textural corners effectively. Furthermore, it can satisfy the demands of real-time applications.

关键词： Harris corner detector MIC detector multigrid algorithm real-time demands

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multigrid Acceleration and Chimera Technique for Viscous Flow Past a Hovering Rotor

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JOURNAL OF AIRCRAFT 2011年第2期48卷 713-715页

作者： Yang, Aiming Yang, Xiaoquan Fudan Univ Dept Engn Sci & Mech Shanghai 200433 Peoples R China

An efficient multigrid algorithm coupled with chimera grids for Navier-Stokes computations about a hovering rotor was investigated. The speed-up ratio with two-level multiple grids was greater than 5.0 for both transonic case and subsonic case. A slight overprediction of the total thrust coefficient was observed for both cases. The convergence criteria was defined as 4 orders of magnitude reduction in density residual, meanwhile the oscillation amplitude of the total thrust coefficient was less than 0.5% of its final value. A slight overprediction was demonstrated for both cases, which was about 6.68% and 2.97%. All these differences in thrust coefficients were mainly due to the imprecise representation of the tip vortex. The holes boundary of the background grid was about one chord away from the blade surface in the normal direction and about half of one chord away from the blade tip in the spanwise direction.

关键词： Incompressible Flow Numerical Integration Vortices Reynolds Averaged Navier Stokes Helicopter Rotor Finite Volume Method multigrid algorithm Baldwin Lomax Turbulence Model Aerodynamic Performance Fluid Density

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Efficient Edge-Based Rotor/Stator Interaction Method

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AIAA JOURNAL 2011年第1期49卷 19-31页

作者： Burgos, Manuel A. Contreras, Jesus Corral, Roque Univ Politecn Cartagena Dept Fluid Dynam Murcia 30006 Spain Ind Turbopropulsores SA Technol & Methods Dept Madrid 28830 Spain

A method to address the rotor/stator interaction problem on an edge-based Reynolds-averaged Navier-Stokes solver is presented. The implementation of the phase-lagged boundary conditions and a new original conservative discretization of the sliding plane in an unstructured solver is discussed in detail. The numerical method is implicit in time, and convergence is accelerated using a multigrid technique where the coarser grids are obtained by agglomeration. Results of the present method are compared with the experimental results obtained at the National Aerospace Laboratory (The Netherlands) for a subsonic fan.

关键词： Rotor Stator Interactions Reynolds Averaged Navier Stokes National Aerospace Laboratories Rotor Blades Static Pressure multigrid algorithm Message Passing Interface Unstructured Grid Unsteady Turbomachinery External Flows

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Critical Study of Agglomerated multigrid Methods for Diffusion

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AIAA JOURNAL 2010年第4期48卷 839-847页

作者： Nishikawa, Hiroaki Diskin, Boris Thomas, James L. Natl Inst Aerosp Hampton VA 23666 USA NASA Langley Res Ctr Computat Aerosci Branch Hampton VA 23681 USA

Agglomerated multigrid techniques used in unstructured-grid methods are studied critically for a model problem representative of laminar diffusion in the incompressible limit. The studied target-grid discretizations and discretizations used on agglomerated grids are typical of current node-centered formulations. Agglomerated multigrid convergence rates are presented using a range of two- and three-dimensional randomly perturbed unstructured grids for simple geometries with isotropic and stretched grids. Two agglomeration techniques are used within an overall topology-preserving agglomeration framework. The results show that a multigrid with an inconsistent coarse-grid scheme using only the edge derivatives (also referred to in the literature as a thin-layer formulation) provides considerable speedup over single-grid methods, but its convergence can deteriorate on highly skewed grids. A multigrid with a Galerkin coarse-grid discretization using piecewise-constant prolongation and a heuristic correction factor is slower and also can be grid dependent. In contrast, nearly grid-independent convergence rates are demonstrated for a multigrid with consistent coarse-grid discretizations. Convergence rates of multigrid cycles are verified with quantitative analysis methods in which parts of the two-grid cycle are replaced by their idealized counterparts.

关键词： multigrid Methods Unstructured Grid Reynolds Averaged Navier Stokes multigrid algorithm High Aspect Ratio Dirichlet Boundary Condition Poisson's Equation Linear Interpolation Unsteady Flows

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Numerical Study of High-Resolution Scheme Based on Preconditioning Method

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JOURNAL OF AIRCRAFT 2009年第2期46卷 520-525页

作者： Xie, Futian Song, Wenping Han, Zhonghua Northwestern Polytech Univ Natl Key Lab Aerodynam Design & Res Xian 710072 Peoples R China

In this paper, an efficient and accurate method based on the preconditioned advection upstream splitting method (AUSM) scheme is studied. Turkel's preconditioning method in conjunction with the second-order finite-volume monotone upwind schemes for conservation laws (MUSCL)-type AUSMDV (a mixture of AUSMD and AUSMV where "D" and "V" denote a flux-difference splitting-biased scheme and flux-vector-splitting-biased one, respectively) and AUSM(+)-up schemes based on the primitive variables is used to solve Navier-Stokes equations. These two schemes used in computational fluid dynamics with or without preconditioning methods are compared. The surface pressure distributions are compared with those calculated from a central difference scheme. The preconditioning method used in this paper obtains an improved convergence, stability, and the capability for the calculation of the low Mach number flows and transonic flows. The preconditioning high-resolution scheme strengthens the capability of identifying discontinuities and reducing the numerical dissipation. The present method that combines the multigrid algorithm further accelerates the convergence. Flow-independent convergence rates of the method are also observed from the numerical results for the low Mach number flows.

关键词： Freestream Mach Number Incompressible Flow Lift Coefficient Stagnation Point Primitive Variable Computational Fluid Dynamics multigrid algorithm multigrid Methods Advection Navier Stokes Equations

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Solving discontinuous Galerkin formulations of Poisson's equation using geometric and p multigrid

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AIAA JOURNAL 2008年第4期46卷 894-902页

作者： Helenbrook, Brian T. Atkins, H. L. Clarkson Univ Dept Mech & Aeronaut Engn Potsdam NY 13699 USA NASA Langley Res Ctr Computat Modeling & Simulat Branch Hampton VA 23681 USA

Methods for solving discontinuous Galerkin formulations of the Poisson equation by coupling p multigrid to geometric multigrid are investigated. The simple approach of performing iterative relaxation on solution approximations of decreasing polynomial degree p down to p = 0 and then applying geometric multigrid is ineffective. The transition from p = 1 top = 0 causes the performance of the entire iteration to degrade because the long wavelength eigenfunctions of the p = 1 discontinuous system are not represented well in the p = 0 space. A new approach is proposed that coarsens from the p = 1 discontinuous space to the p = 1 continuous space. This approach eliminates the problems caused by the p = 1 to p = 0 transition. Furthermore, the p = 1 continuous space is a standard finite element space for which geometric multigrid is well-defined. In addition, when the discontinuous Galerkin equations are restricted to a continuous space, one recovers the Galerkin formulation of continuous finite elements. Thus, applying geometric multigrid to this system is straightforward and effective. Numerical tests agree well with the analysis and confirm that the new approach gives rapid convergence rates that are grid-independent and only weakly sensitive to the polynomial order.

关键词： Poisson's Equation Finite Element Formulation multigrid algorithm High Aspect Ratio Finite Volume Scheme Dirichlet Boundary Condition Discrete Poisson Equation Navier Stokes Equations Numerical algorithms Heat Equations

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