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.
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