Implicit LU-SGS algorithm for high-order methods on unstructured grid with p-multigrid strategy for solving steady Navier-Stokes equations

Matteo Parsani, Kris Van Den Abeele, Christian Lacor, Eli Turkel, G. Tryggvason (Editor)

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

The fluid dynamic equations are discretized by a high-order spectral
volume (SV) method on unstructured tetrahedral grids. We solve the
steady state equations by advancing in time using a backward Euler
(BE) scheme. To avoid the inversion of a large matrix we approximate
BE by an implicit lower-upper symmetric Gauss-Seidel (LU-SGS)
algorithm. The implicit method addresses the stiffness in the
discrete Navier-Stokes equations associated with stretched meshes.
The LU-SGS algorithm is then used as a smoother for a $p$-multigrid
approach. A Von Neumann stability analysis is applied to the two
dimensional linear advection equation to determine its damping
properties. The implicit LU-SGS scheme is used to solve the
two dimensional (2D) compressible laminar Navier-Stokes equations.
We compute the solution of a laminar external flow over a cylinder and around an airfoil at low Mach number. We compare the convergence
rates with explicit Runge-Kutta (E-RK) schemes employed as a smoother.
The effects of the cell aspect ratio and the low Mach number on the convergence are investigated.
With the $p$-multigrid method and the implicit smoother the
computational time can be reduced by a factor of up to $5-10$ compared
with a well tuned E-RK scheme.
Original languageEnglish
Pages (from-to)828-850
Number of pages22
JournalJournal of Computational Physics
Volume229
Issue number3
Publication statusPublished - 9 Sep 2010

Bibliographical note

G. Tryggvason

Keywords

  • Navier-Stokes
  • High-order Methods
  • Implicit LU-SGS algorithm
  • Von Neumann analysis
  • p-multigrid

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