Journal of Theoretical
and Applied Mechanics

42, 4, pp. 869-903, Warsaw 2004

Computations of an unsteady viscous flow in a three-dimensional system of ducts. Part II: Implementation of the spectral element method and sample results

Jacek Szumbarski, Piotr Olszewski, Konrad Wawruch, Zbigniew Małota
The second part the paper focuses on implementation issues of the spectral element technique and presents sample results of numerical simulations. Particular algorithms like preconditioning of the presser solver, fast diagonalization method and the projection method for solving sequences of large linear systems are described in some details. The computational results, obtained for both test domains and geometries of medical origin, are presented. The comparison with the results of computations with the FIDAP package is provided. The difficulties and limitations of the spectral method and current implementation are discussed. Attempts of the parallelization of the spectral code and the obtained efficiency are briefly described.
Keywords: Navier-Stokes equations; spectral element methods; pressure preconditioners; fast diagonalization; parallel computations