Author: Publisher:
ISBN:
Category : Astronautics
Languages : en
Pages : 182
Book Description
NASA Langley Scientific and Technical Information Output: 1999
Author: Multiscale and Multiresolution Methods
Author: Timothy J. BarthPublisher: Springer Science & Business Media
ISBN: 3642562051
Category : Mathematics
Languages : en
Pages : 396
Book Description
Many computionally challenging problems omnipresent in science and engineering exhibit multiscale phenomena so that the task of computing or even representing all scales of action is computationally very expensive unless the multiscale nature of these problems is exploited in a fundamental way. Some diverse examples of practical interest include the computation of fluid turbulence, structural analysis of composite materials, terabyte data mining, image processing, and a multitude of others. This book consists of both invited and contributed articles which address many facets of efficient multiscale representation and scientific computation from varied viewpoints such as hierarchical data representations, multilevel algorithms, algebraic homogeni- zation, and others. This book should be of particular interest to readers interested in recent and emerging trends in multiscale and multiresolution computation with application to a wide range of practical problems.
Robust Multigrid Algorithms for the Incompressible Navier-Stokes Equations
Author: Ruben S. MonteroPublisher:
ISBN:
Category : Anisotropy
Languages : en
Pages : 26
Book Description
Anisotropies occur naturally in CFD where the simulation of small scale physical phenomena, such as boundary layers at high Reynolds numbers, causes the grid to be highly stretched leading to a slow down in convergence of multigrid methods. Several approaches aimed at making multigrid a robust solver have been proposed and analyzed in literature using the scalar diffusion equation. However, they have been rarely applied to solving more complicated models, like the incompressible Navier-Stokes equations. This paper contains the first published numerical results of the behavior of two popular robust multigrid approaches (alternating-plane smoothers combined with standard coarsening and plane implicit smoothers combined with semi-coarsening) for solving the 3-D incompressible Navier-Stokes equations in the simulation of the driven cavity and a boundary layer over a flat plate on a stretched grid. The discrete operator is obtained using a staggered-grid arrangement of variables with a finite volume technique and second-order accuracy is achieved using defect correction within the multigrid cycle. Grid size, grid stretching and Reynolds number are the factors considered in evaluating the robustness of the multigrid methods. Both approaches yield large increases in convergence rates over cell-implicit smoothers on stretched grids. The combination of plane implicit smoothers and semi-coarsening was found to be fully robust in the fiat plate simulation up to Reynolds numbers 10(exp 6) and the best alternative in the driven cavity simulation for Reynolds numbers above 10(exp 3). The alternating-plane approach exhibits a better behavior for lower Reynolds numbers (below to 10(exp 3) in the driven cavity simulation. A parallel variant of the smoother, tri-plane ordering, presents a good trade-off between convergence and parallel properties.
Opportunities for Breakthroughs in Large-Scale Computational Simulation and Design
Author: Publisher:
ISBN:
Category : Geometrical models
Languages : en
Pages : 30
Book Description
Opportunities for breakthroughs in the large-scale computational simulation and design of aerospace vehicles are presented. Computational fluid dynamics tools to be used within multidisciplinary analysis and design methods are emphasized. The opportunities stem from speedups and robustness improvements in the underlying unit operations associated with simulation (geometry modeling, grid generation, physical modeling, analysis, etc.). Further, an improved programming environment can synergistically integrate these unit operations to leverage the gains. The speedups result from reducing the problem setup time through geometry modeling and grid generation operations, and reducing the solution time through the operation counts associated with solving the discretized equations to a sufficient accuracy. The opportunities are addressed only at a general level here, but an extensive list of references containing further details is included.
Frontiers of Computational Fluid Dynamics 2002
Author: David A. CaugheyPublisher: World Scientific
ISBN: 9810248490
Category : Science
Languages : en
Pages : 523
Book Description
This series of volumes on the ?Frontiers of Computational Fluid Dynamics? was introduced to honor contributors who have made a major impact on the field. The first volume was published in 1994 and was dedicated to Prof Antony Jameson; the second was published in 1998 and was dedicated to Prof Earl Murman. The volume is dedicated to Prof Robert MacCormack.The twenty-six chapters in the current volume have been written by leading researchers from academia, government laboratories, and industry. They present up-to-date descriptions of recent developments in techniques for numerical analysis of fluid flow problems, and applications of these techniques to important problems in industry, as well as the classic paper that introduced the ?MacCormack scheme? to the world.
PETSc for Partial Differential Equations: Numerical Solutions in C and Python
Author: Ed BuelerPublisher: SIAM
ISBN: 1611976316
Category : Mathematics
Languages : en
Pages : 407
Book Description
The Portable, Extensible Toolkit for Scientific Computation (PETSc) is an open-source library of advanced data structures and methods for solving linear and nonlinear equations and for managing discretizations. This book uses these modern numerical tools to demonstrate how to solve nonlinear partial differential equations (PDEs) in parallel. It starts from key mathematical concepts, such as Krylov space methods, preconditioning, multigrid, and Newton’s method. In PETSc these components are composed at run time into fast solvers. Discretizations are introduced from the beginning, with an emphasis on finite difference and finite element methodologies. The example C programs of the first 12 chapters, listed on the inside front cover, solve (mostly) elliptic and parabolic PDE problems. Discretization leads to large, sparse, and generally nonlinear systems of algebraic equations. For such problems, mathematical solver concepts are explained and illustrated through the examples, with sufficient context to speed further development. PETSc for Partial Differential Equations addresses both discretizations and fast solvers for PDEs, emphasizing practice more than theory. Well-structured examples lead to run-time choices that result in high solver performance and parallel scalability. The last two chapters build on the reader’s understanding of fast solver concepts when applying the Firedrake Python finite element solver library. This textbook, the first to cover PETSc programming for nonlinear PDEs, provides an on-ramp for graduate students and researchers to a major area of high-performance computing for science and engineering. It is suitable as a supplement for courses in scientific computing or numerical methods for differential equations.
SIAM Journal on Scientific Computing
Author: NASA Langley Scientific and Technical Information Output-2001
Author: A Parallel Multigrid Solver for Viscous Flows on Anisotropic Structured Grids
Author: Manuel PrietoPublisher:
ISBN:
Category : Multigrid methods (Numerical analysis)
Languages : en
Pages : 26
Book Description
Abstract: "This paper presents an efficient parallel multigrid solver for speeding up the computation of a 3-D model that treats the flow of a viscous fluid over a flat plate. The main interest of this simulation lies in exhibiting some basic difficulties that prevent optimal multigrid efficiencies from being achieved. As the computing platform, we have used Coral, a Beowulf-class system based on Intel Pentium processors and equipped with GigaNet cLAN and switched Fast Ethernet networks. Our study not only examines the scalability of the solver but also includes a performance evaluation of Coral where the investigated solver has been used to compare several of its design choices, namely, the interconnection network (GigaNet versus switched Fast-Ethernet) and the node configuration (dual nodes versus single nodes). As a reference, the performance results have been compared with those obtained with the NAS-MG benchmark."
Semicoarsening and Implicit Smoothers for the Simulation of a Flat Plate at Yaw
Author: Ruben S. MonteroPublisher:
ISBN:
Category : Multigrid methods (Numerical analysis)
Languages : en
Pages : 24
Book Description
This paper presents a full multigrid solver for the simulation of flow over a yawed at plate. The two problems associated with this simulation; boundary layers and entering flows with non-aligned characteristics, have been successfully overcome through the combination of a plane-implicit solver and semicoarsening. In fact, this multigrid algorithm exhibits a textbook multigrid convergence rate, i.e., the solution of the discrete system of equations is obtained in a fixed amount of computational work, independently of the grid size, grid stretching factor and non-alignment parameter. Also, a parallel variant of the smoother based on a four-color ordering of planes is investigated.