High-Order Schemes for Navier-Stokes Equations: Algorithm and Implementation Into FDL3DI

Abstract

A spectrum of higher-order schemes is developed to solve the Navier-Stokes equations in finite-difference formulations. Pade type formulas of up to sixth order with a five-point stencil are developed for the difference scheme. Viscous terms are treated by successive applications of the first derivative operator. However, formulas are also derived for use in a mid-point interpolation-differentiation strategy. For numerical stability, up to tenth-order filtering schemes are developed. The spectral properties of the differentiation and filtering schemes are examined and guidelines are provided to choose proper filter coefficients. Special high-order formulas are obtained for differentiation and filtering in the vicinity of boundaries. The coefficients required for systematic implementation of Neumann-type boundary conditions are also presented. A brief description is provided of the manner in which the FDL3DI code is enhanced by coupling the approximately-factored procedure with these compact-difference based algorithms and by incorporating an explicit fourth-order Runge-Kutta scheme.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1998
Accession Number
ADA364301

Entities

People

  • Datta V. Gaitonde
  • Miguel R. Visbal

Organizations

  • Air Force Research Laboratory

Tags

Communities of Interest

  • Air Platforms
  • Space

DTIC Thesaurus Topics

  • Air Force Research Laboratories
  • Aircrafts
  • Algorithms
  • Boundaries
  • Boundary Layer
  • Computational Fluid Dynamics
  • Computational Science
  • Differential Equations
  • Equations
  • Filtration
  • Fluid Mechanics
  • Interpolation
  • Navier Stokes Equations
  • Numerical Analysis
  • Partial Differential Equations
  • Turbulent Mixing
  • Wave Phenomena

Fields of Study

  • Physics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)