2,233 research outputs found

    Spectral methods for CFD

    Get PDF
    One of the objectives of these notes is to provide a basic introduction to spectral methods with a particular emphasis on applications to computational fluid dynamics. Another objective is to summarize some of the most important developments in spectral methods in the last two years. The fundamentals of spectral methods for simple problems will be covered in depth, and the essential elements of several fluid dynamical applications will be sketched

    Domain decomposition methods for the parallel computation of reacting flows

    Get PDF
    Domain decomposition is a natural route to parallel computing for partial differential equation solvers. Subdomains of which the original domain of definition is comprised are assigned to independent processors at the price of periodic coordination between processors to compute global parameters and maintain the requisite degree of continuity of the solution at the subdomain interfaces. In the domain-decomposed solution of steady multidimensional systems of PDEs by finite difference methods using a pseudo-transient version of Newton iteration, the only portion of the computation which generally stands in the way of efficient parallelization is the solution of the large, sparse linear systems arising at each Newton step. For some Jacobian matrices drawn from an actual two-dimensional reacting flow problem, comparisons are made between relaxation-based linear solvers and also preconditioned iterative methods of Conjugate Gradient and Chebyshev type, focusing attention on both iteration count and global inner product count. The generalized minimum residual method with block-ILU preconditioning is judged the best serial method among those considered, and parallel numerical experiments on the Encore Multimax demonstrate for it approximately 10-fold speedup on 16 processors

    Iterative Methods for Problems in Computational Fluid Dynamics

    Get PDF
    We discuss iterative methods for solving the algebraic systems of equations arising from linearization and discretization of primitive variable formulations of the incompressible Navier-Stokes equations. Implicit discretization in time leads to a coupled but linear system of partial differential equations at each time step, and discretization in space then produces a series of linear algebraic systems. We give an overview of commonly used time and space discretization techniques, and we discuss a variety of algorithmic strategies for solving the resulting systems of equations. The emphasis is on preconditioning techniques, which can be combined with Krylov subspace iterative methods. In many cases the solution of subsidiary problems such as the discrete convection-diffusion equation and the discrete Stokes equations plays a crucial role. We examine iterative techniques for these problems and show how they can be integrated into effective solution algorithms for the Navier-Stokes equations

    Schnelle Löser für partielle Differentialgleichungen

    Get PDF
    The workshop Schnelle Löser für partielle Differentialgleichungen, organised by Randolph E. Bank (La Jolla), Wolfgang Hackbusch(Leipzig), Gabriel Wittum (Heidelberg) was held May 22nd - May 28th, 2005. This meeting was well attended by 47 participants with broad geographic representation from 9 countries and 3 continents. This workshop was a nice blend of researchers with various backgrounds
    corecore