Upwind discretization of the steady Navier-Stokes equations

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    A discretization method is presented for the full, steady, compressible Navier-Stokes equations. The method makes use of quadrilateral finite volumes and consists of an upwind discretization of the convective part and a central discretization of the diffusive part. In the present paper the emphasis lies on the discretization of the convective part. The solution method applied solves the steady equations directly by means of a non-linear relaxation method accelerated by multigrid. The solution method requires the discretization to be continuously differentiable. For two upwind schemes which satisfy this requirement, results of a quantitative error analysis are presented. Osher's scheme appears to be increasingly more accurate than van Leer's scheme with increasing Reynolds number. A suitable higher-order accurate discretization of the convection terms is derived. On the basis of this higher-order scheme, to preserve monotonicity, a new limiter is constructed. Additional aspects of the subject are discussed.
    Original languageEnglish
    Pages (from-to)99-117
    JournalInternational Journal for Numerical Methods in Fluids
    Issue number1
    Publication statusPublished - 1990


    • Convective Flow
    • Finite Volume Method
    • Multigrid Methods
    • Navier-Stokes Equation
    • Steady Flow
    • Diffusion
    • Error Analysis
    • Gas Dynamics
    • Relaxation Method (Mathematics)
    • Upstream


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