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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of engineering mathematics 38 (2000), S. 403-426 
    ISSN: 1573-2703
    Keywords: polynomial preconditioning ; conservation laws ; implicit timestepping ; aerodynamic flows
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract Polynomial preconditioners which are suitable in implicit time-stepping methods for conservation laws are reviewed and analyzed. The preconditioners considered are either based on a truncation of a Neumann series or on Chebyshev polynomials for the inverse of the system-matrix. The latter class of preconditioner is optimal in a space of polynomials of certain degree if the matrix has only real eigenvalues and a non-singular system of eigenvectors. The preconditioning can be applied to any convergent splitting of the system matrix, i.e. to any classical implicit time-stepping method for conservation laws that is based on a quasi-Newton iteration. An efficient implementation based on SSOR is presented and the approach is applied to simulations of the viscous unsteady Burgers equation and to inviscid steady flow around an airfoil in two spatial dimensions to illustrate the method in large-scale computations. For viscous flows the efficiency increase due to preconditioning is considerable.
    Type of Medium: Electronic Resource
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