Parallel solution of the instationary incompressible Navier-Stokes equations
type: Item
instance of: scholarly article
zbMATH Open document ID: 1027.76001
author: Hubertus Oswald
publication date: 2001-11-12T00:00:00Z
Mathematics Subject Classification ID: 76-02
Mathematics Subject Classification ID: 76M10
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 65Y05
zbMATH DE Number: 1671895
zbMATH Keywords: parallelization
zbMATH Keywords: non-stationary incompressible Navier-Stokes equations
zbMATH Keywords: multigrid method
zbMATH Keywords: anisotropic meshes
zbMATH Keywords: nonconformiing finite element method
zbMATH Keywords: upwinding
zbMATH Keywords: stabilization
zbMATH Keywords: Glowinski's fractional step theta-scheme
zbMATH Keywords: Kan's projection method
zbMATH Keywords: fixed-point defect-correction method
zbMATH Keywords: coarse grid
zbMATH Keywords: lid-driven cavity
zbMATH Keywords: flow around cylinder
zbMATH Keywords: C++ class library ParFlow++
MaRDI profile type: Publication
title: Parallel solution of the instationary incompressible Navier-Stokes equations
review text: This work is concerned with combination of multigrid and parallelization techniques for solving the non-stationary, incompressible Navier-Stokes problem, especially on anisotropic meshes. The main focus is on aspects of implementation and efficiency. NEWLINENEWLINENEWLINEThe Navier-Stokes equations are firstly discretized in space by a non-conforming finite element method that is based upon a triangulation into hexahedrons, rotated trilinear ansatz functions for the velocity, and a piecewise constant pressure approximation. For stabilization, simple and Samarskij upwinding are employed. The time discretization relies upon Glowinski's fractional step \(\theta\)-scheme, and the velocity and pressure problem are decoupled by van Kan's projection method. The nonlinear problems are solved with a fixed-point defect-correction method. A detailed analysis of the spatial discretization can be found in [\textit{F. Schieweck}, Parallele Lösung der stationären inkompressiblen Navier-Stokes Gleichungen. (Parallel solution of the stationary incompressible Navier-Stokes equations). (German) Magdeburg: Univ. Magdeburg, Fakultät Mathematik (1997; Zbl 0915.76051)]. NEWLINENEWLINENEWLINEThe parallelization is based upon a partition of the coarse grid. The resulting parallel blocks are then uniformly refined. The author compares the suggested parallel multigrid method with its sequential counterpart; they differ only in the smoothing process. NEWLINENEWLINENEWLINEIt turns out that the parallel method is essentially of the same numerical efficiency as the corresponding sequential method. However, the choice of the coarse grid (in particular, the relation of the numbers of coarse grid elements and processors) strongly influences the parallel efficiency. The best results are obtained for the parallel CG-method with multiplicative multigrid for the preconditioning. NEWLINENEWLINENEWLINEThe method suggested is tested on lid-driven cavity problem with a Reynolds number \(Re = 3200\), and on …
reviewed by: Etienne Emmrich
description: scientific article; zbMATH DE number 1671895