Local solution acceleration method for the Euler and Navier-Stokes equations

D. Drikakis, S. Tsangaris

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

The solution of the compressible Euler and Navier-Stokes equations via un upwind finite volume scheme is obtained. For the inviscid fluxes, the monotone upstream-centered scheme for conservation laws (MUSCL) has been incorporated into a Riemann solver. The MUSCL scheme is used for the unfactored implicit equations that are solved by a Newton form, and relaxation is performed via Gauss-Seidel relaxation technique. The solution on the fine grid is obtained by iterating first on a sequence of coarser grids and then interpolating the solution up to the next refined grid. Since the distribution of the numerical error is nonuniform, the local solution of the equations can be obtained in regions where the numerical errors are large. The construction of the partial meshes, in which the iterations will be continued, is determined by an adaptive procedure taking into account some convergence criteria. Reduction of the computational work units for two-dimensional problems is obtained via the local adaptive mesh solution which is expected to be more effective in three-dimensional complex flow computations.
Original languageUndefined/Unknown
Pages (from-to)340-348
Number of pages9
JournalAIAA Journal
Volume30
Issue number2
DOIs
Publication statusPublished - 1 Feb 1992

Keywords

  • aerodynamics
  • wings
  • airfoils
  • computer programming
  • algorithms
  • computer software
  • mathematical techniques
  • iterative methods
  • Euler equations
  • Gauss-Seidel relaxation
  • local solution acceleration method
  • Navier-Stokes equations
  • flow of fluids
  • solution

Cite this

Drikakis, D. ; Tsangaris, S. / Local solution acceleration method for the Euler and Navier-Stokes equations. In: AIAA Journal. 1992 ; Vol. 30, No. 2. pp. 340-348.
@article{d4c77f721a0846708516e09df068b494,
title = "Local solution acceleration method for the Euler and Navier-Stokes equations",
abstract = "The solution of the compressible Euler and Navier-Stokes equations via un upwind finite volume scheme is obtained. For the inviscid fluxes, the monotone upstream-centered scheme for conservation laws (MUSCL) has been incorporated into a Riemann solver. The MUSCL scheme is used for the unfactored implicit equations that are solved by a Newton form, and relaxation is performed via Gauss-Seidel relaxation technique. The solution on the fine grid is obtained by iterating first on a sequence of coarser grids and then interpolating the solution up to the next refined grid. Since the distribution of the numerical error is nonuniform, the local solution of the equations can be obtained in regions where the numerical errors are large. The construction of the partial meshes, in which the iterations will be continued, is determined by an adaptive procedure taking into account some convergence criteria. Reduction of the computational work units for two-dimensional problems is obtained via the local adaptive mesh solution which is expected to be more effective in three-dimensional complex flow computations.",
keywords = "aerodynamics, wings, airfoils, computer programming, algorithms, computer software, mathematical techniques, iterative methods, Euler equations, Gauss-Seidel relaxation, local solution acceleration method, Navier-Stokes equations , flow of fluids, solution",
author = "D. Drikakis and S. Tsangaris",
note = "cited By 3",
year = "1992",
month = "2",
day = "1",
doi = "10.2514/3.10924",
language = "Undefined/Unknown",
volume = "30",
pages = "340--348",
journal = "AIAA Journal",
issn = "0001-1452",
number = "2",

}

Local solution acceleration method for the Euler and Navier-Stokes equations. / Drikakis, D.; Tsangaris, S.

In: AIAA Journal, Vol. 30, No. 2, 01.02.1992, p. 340-348.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Local solution acceleration method for the Euler and Navier-Stokes equations

AU - Drikakis, D.

AU - Tsangaris, S.

N1 - cited By 3

PY - 1992/2/1

Y1 - 1992/2/1

N2 - The solution of the compressible Euler and Navier-Stokes equations via un upwind finite volume scheme is obtained. For the inviscid fluxes, the monotone upstream-centered scheme for conservation laws (MUSCL) has been incorporated into a Riemann solver. The MUSCL scheme is used for the unfactored implicit equations that are solved by a Newton form, and relaxation is performed via Gauss-Seidel relaxation technique. The solution on the fine grid is obtained by iterating first on a sequence of coarser grids and then interpolating the solution up to the next refined grid. Since the distribution of the numerical error is nonuniform, the local solution of the equations can be obtained in regions where the numerical errors are large. The construction of the partial meshes, in which the iterations will be continued, is determined by an adaptive procedure taking into account some convergence criteria. Reduction of the computational work units for two-dimensional problems is obtained via the local adaptive mesh solution which is expected to be more effective in three-dimensional complex flow computations.

AB - The solution of the compressible Euler and Navier-Stokes equations via un upwind finite volume scheme is obtained. For the inviscid fluxes, the monotone upstream-centered scheme for conservation laws (MUSCL) has been incorporated into a Riemann solver. The MUSCL scheme is used for the unfactored implicit equations that are solved by a Newton form, and relaxation is performed via Gauss-Seidel relaxation technique. The solution on the fine grid is obtained by iterating first on a sequence of coarser grids and then interpolating the solution up to the next refined grid. Since the distribution of the numerical error is nonuniform, the local solution of the equations can be obtained in regions where the numerical errors are large. The construction of the partial meshes, in which the iterations will be continued, is determined by an adaptive procedure taking into account some convergence criteria. Reduction of the computational work units for two-dimensional problems is obtained via the local adaptive mesh solution which is expected to be more effective in three-dimensional complex flow computations.

KW - aerodynamics

KW - wings

KW - airfoils

KW - computer programming

KW - algorithms

KW - computer software

KW - mathematical techniques

KW - iterative methods

KW - Euler equations

KW - Gauss-Seidel relaxation

KW - local solution acceleration method

KW - Navier-Stokes equations

KW - flow of fluids

KW - solution

UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-0026816832&partnerID=40&md5=a7429b1acc4f84e2aa847251010be1d7

U2 - 10.2514/3.10924

DO - 10.2514/3.10924

M3 - Article

VL - 30

SP - 340

EP - 348

JO - AIAA Journal

JF - AIAA Journal

SN - 0001-1452

IS - 2

ER -