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Parallelizing FLITE3D - a multigrid finite element Euler solver

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS 2001年第7期35卷 809-827页

作者： Hu, YF Emerson, DR Ashworth, M Maguire, KCF Blake, RJ CLRC Daresbury Lab Warrington WA4 4AD Cheshire England

FLITE3D is a multigrid Euler solver. It is used extensively by British Aerospace in aircraft design and simulation. This paper presents experiences in parallelizing this industrial code. Owing to the employment of an agglomeration-based multigrid technique, the communication overhead on the coarser meshes could readily erode any gain from the use of parallel computers. The parallelization of the code therefore required careful design and implementation. The strategy adopted in the parallelization of the code, including the use of data structures and communication primitives, is described. Numerical results are presented to demonstrate the efficiency of the resulting parallel code. Copyright (C) 2001 John Wiley & Sons, Ltd.

关键词： multigrid algorithm parallel computing unstructured mesh

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A hybrid domain decomposition and multigrid method for the acceleration of compressible viscous flow calculations on unstructured triangular meshes

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INTERNATIONAL JOURNAL OF COMPUTATIONAL FLUID DYNAMICS 2001年第4期14卷 287-304页

作者： Dolean, V Lanteri, S INRIA Sophia Antipolis Projet Sinus F-06902 Sophia Antipolis France

This paper is concerned with the formulation and the evaluation of a hybrid solution method that makes use of domain decomposition and multigrid principles for the calculation of two-dimensional compressible viscous flows on unstructured triangular meshes. More precisely, a non-overlapping additive domain decomposition method is used to coordinate concurrent subdomain solutions with a multigrid method. This hybrid method is developed in the context of a flow solver for the Navier-Stokes equations which is based on a combined finite element/finite volume formulation on unstructured triangular meshes. Time integration of the resulting semi-discrete equations is performed using a linearized backward Euler implicit scheme. As a result, each pseudo time step requires the solution of a sparse linear system. In this study, a non-overlapping domain decomposition algorithm is used for advancing the solution at each implicit time step. Algebraically, the Schwarz algorithm is equivalent to a Jacobi iteration on a linear system whose matrix has a block structure. A substructuring technique can be applied to this matrix in order to obtain a fully implicit scheme in terms of interface unknowns. In the present approach, the interface unknowns are numerical fluxes. The interface system is solved by means of a full GMRES method. Here, the local system solves that are induced by matrix-vector products with the interface operator, are performed using a multigrid by volume agglomeration method. The resulting hybrid domain decomposition and multigrid solver is applied to the computation of several steady flows around a geometry of NACA0012 airfoil.

关键词： domain decomposition method Navier-Stokes equations finite elements finite volumes triangular meshes multigrid algorithm parallel computing

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Optimal control of non-isothermal viscoelastic fluid flow

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JOURNAL OF NON-NEWTONIAN FLUID MECHANICS 2000年第3期88卷 261-301页

作者： Kunisch, K Marduel, X Karl Franzens Univ Graz Inst Math A-8010 Graz Austria

Optimal control of viscoelastic fluid flow in a 4 to 1 contracting channel is investigated. The control mechanism is based on heating or cooling the fluid along a portion of the boundary of the flow domain. In order to perform the control, a nonisothermal model for viscoelastic fluids is used consisting of the PTT model with relaxation time and elastic viscosity depending on temperature (following an exponential dependency, the WLF model). Moreover, the momentum, mass and constitutive equations are coupled with the heat equation forming the so-called primal system. The goal of the control is to find an optimal temperature on the boundary of the domain such that the large recirculation zones at the corners of the contracting channel are reduced and the fluid behaves like a viscous one. Two different cost functionals are used to reach this goal: one of tracking type, the other penalizing negative contributions of the velocity component in direction of the span of the channel. The minimization of these cost functionals is achieved with a gradient algorithm. An optimality system, derived by the use of the Lagrange multipliers, allows us to deduce this optimal control. The primal and dual systems are solved using the same numerical method: a finite differences discretization on staggered grids, a decoupling approach and the Gauss-Seidel solver with a multigrid algorithm. Numerical simulations are performed with a Weissenberg number equal to 10. We succeed in reducing the recirculation zone by applying the correct boundary temperature. (C) 2000 Elsevier Science B.V. All rights reserved.

关键词： optimal control adjoint system finite differences multigrid algorithm PTT model non-isothermal flows viscoelastic flow

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Parallel linear multigrid by agglomeration for the acceleration of 3D compressible flow calculations on unstructured meshes

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NUMERICAL algorithmS 2000年第4期24卷 309-332页

作者： Carré, G Lanteri, S INRIA F-06902 Sophia Antipolis France

In this paper, we report on our recent efforts concerning the design of parallel linear multigrid algorithms for the acceleration of 3-dimensional compressible flow calculations. The multigrid strategy adopted in this study relies on a volume agglomeration principle for the construction of the coarse grids starting from a fine discretization of the computational domain. In the past, this strategy has mainly been studied in the 2-dimensional case for the solution of the Euler equations (see Lallemand et al. [6]), the laminar Navier-Stokes equations (see Mavriplis and Venkatakrishnan [12]) and the turbulent Navier-Stokes equations (see Carre [1], Mavriplis [10] and Francescatto and Dervieux [4]). A first extension to the 3-dimensional case is presented by Mavriplis and Venkatakrishnan in [13] and more recently in Mavriplis and Pirzadeh [11]. The main contribution of the present work is twofold: on the one hand, we demonstrate the successful extension and application of the multigrid by a volume agglomeration principle to the acceleration of complex 3-dimensional flow calculations on unstructured tetrahedral meshes and, on the other hand, we enhance further the efficiency of the methodology through its adaptation to parallel architectures. Moreover, a nontrivial aspect of this work is that the corresponding software developments are taking place in an existing industrial flow solver.

关键词： computational fluid dynamics Navier-Stokes equations finite element method finite volume method multigrid algorithm parallel computing

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Multiplicative Schwarz algorithms for the Galerkin boundary element method

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SIAM JOURNAL ON NUMERICAL ANALYSIS 2000年第4期38卷 1243-1268页

作者： Maischak, M Stephan, EP Tran, T Univ Hannover Inst Appl Math D-30167 Hannover Germany Univ New S Wales Sch Math Sydney NSW 2052 Australia

We study the multiplicative Schwarz method for the h- and the p-version Galerkin boundary element method for a hypersingular and a weakly singular integral equation of the rst kind. For both integral equations we prove that the contraction rate of the multiplicative Schwarz operator is strictly less than 1 for the h- version for the two level and the multilevel methods, whereas for the p-version we show that the contraction rate approaches one only logarithmically in p for the 2-level method. Computational results are presented for both the h-version and the p-version which support our theory.

关键词： h-version Galerkin boundary element method p-version Galerkin boundary element method multiplicative Schwarz multigrid algorithm

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Finite element adaptive multigrid Euler solver for rotary wing aerodynamics

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AIAA JOURNAL 2000年第1期38卷 50-56页

作者： Bottasso, CL Shephard, MS Politecn Milan Dipartimento Ingn Aerosp I-20158 Milan Italy Rensselaer Polytech Inst Sci Computat Res Ctr Johnson Chair Engn Troy NY 12180 USA

We present a multigrid strategy for the solution of the Euler equations in three-dimensional domains, The procedures include data structures and mesh modification tools for defining unstructured adaptive multilevel meshes on general curved domains and an implicit time-marching multigrid finite element solver. The code is equipped with special features for the solution of problems relevant to rotorcraft technology, The approach is applied to the simulation of hovering rotors, and the numerical results are compared with experimental data and with numerical simulations obtained using a mesh adaptive single-grid generalized minimal residual (GMRES) solver.

关键词： Rotary Wing Aerodynamics multigrid algorithm Courant Friedrichs Lewy Euler Equations Discontinuous Galerkin Method Shape Functions Aspect Ratio Helicopters Computing Performance

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Development of O(Nm²) preconditioned multigrid solvers for Euler and Navier-Stokes equations

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AIAA JOURNAL 2000年第4期38卷 717-720页

作者： Edwards, JR Thomas, JL N Carolina State Univ Dept Mech & Aerosp Engn Raleigh NC 27695 USA NASA Langley Res Ctr Computat Modeling & Simulat Branch Hampton VA 23681 USA

The development of an efficient, preconditioned implicit multigrid method is described. Results obtained indicate that the combination of time-derivative preconditioning, iteratively improved alternating-direction implicit (ADI) factorization, and defect-correction multigrid can result in very high rates of convergence, essentially independent of mesh size and freestream Mach number.

关键词： Navier Stokes Calculations Freestream Mach Number CFL3D Strouhal Number Courant Friedrichs Lewy NACA 0012 multigrid algorithm Primitive Variable multigrid Methods Angle of Attack

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Computations of transonic turbulent flow past airfoils using multigrid/Bi-CGSTAB algorithm

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AIAA JOURNAL 1999年第1期37卷 118-121页

作者： Lin, H Chieng, CC Chung Shan Inst Technol Aerodynam Branch Lungtan 32500 Taiwan Natl Tsing Hua Univ Dept Engn & Syst Sci Hsinchu 30043 Taiwan

A numerical model solving the full Navier-Stokes equation with the Baldwin-Barth one-equation model of turbulence past an airfoil is developed. The numerical method is based on a finite volume, total variation diminishing (TVD) spatial discretization and is integrated by an implicit unfactored method with preconditioned Bi-CGSTAB algorithm matrix solvers with multigrid acceleration. The test cases demonstrate good lift/drag predictive capability, as well as the efficiency and robustness of the convergence for transonic turbulent flow past an RAE2822 subcritical airfoil and a Cast supercritical airfoil.

关键词： Turbulent Flow Angle of Attack Numerical Modeling multigrid algorithm Freestream Mach Number Total Variation Diminishing Biconjugate Gradient Turbulence Models Euler Equations Eddy Viscosity

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Large-scale parallel unstructured mesh computations for three-dimensional high-lift analysis

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JOURNAL OF AIRCRAFT 1999年第6期36卷 987-998页

作者： Mavriplis, DJ Pirzadeh, S NASA Langley Res Ctr Configurat Aerodynam Branch Hampton VA 23681 USA

A complete geometry to drag polar analysis capability for three-dimensional high-lift configurations is described. The approach is based on the use of unstructured meshes to enable rapid turnaround for complicated geometries that arise in high-lift configurations. Special attention is devoted to creating a capability for enabling analyses on highly resolved grids. Unstructured meshes of several million vertices are initially generated on a workstation and subsequently are refined on a supercomputer. The Row is solved on these refined meshes on large parallel computers using an unstructured agglomeration multigrid algorithm. Good prediction of lift and drag throughout the range of incidences is demonstrated on a transport takeoff configuration using up to 24.7 x 10(6) grid points. The feasibility of using this approach in a production environment on existing parallel machines is demonstrated, as well as the scalability of the solver on machines using up to 1450 processors.

关键词： multigrid algorithm Supercomputers Parallel Computers Freestream Mach Number Angle of Attack Unstructured Grid Aspect Ratio Tetrahedral Element Fuselages Courant Friedrichs Lewy

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The Multi-Grid Block Gauss *** Multipole Method In Electrically Large Problem

The Multi-Grid Block Gauss *** Multipole Method In Electrica...

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1999 International Conference on Computational Electromagnetics and Its Applications(ICCEA’99)

作者： Xu Yuan Fang Dagang Department of Electrical Engineering Nanjing University of Science and Technology

In this paper,we applied FMM to Block Gauss iteration and used this new iteration algorithm as the relaxation scheme in the multi-grid scheme, which is termed as multi-grid block Gauss Seidel fast multipole method(MGB... 详细信息

ISBN: (纸本)0780358023

关键词： Fast multipole method multigrid algorithm Block Gauss Seidel

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