Compact explicit finite-difference approximations to the Navier-Stokes equations

  • S. C. R. Dennis
Invited Lectures
Part of the Lecture Notes in Physics book series (LNP, volume 218)


A review is given of some methods of obtaining explicit compact finite-difference formulae which approximate operators of the type occurring in the Navier-Stokes equations governing the motion of in compressible fluids. In their original form the coefficients which multiply the dependent variable in the formulae contain exponentials, but these can be removed by suitable expansions giving formulae with generally satisfactory computational properties. The results are developed first for operators in one space dimension and can then at once be extended to more space dimensions and time by suitable combination techniques. Approximations in which the truncation error can be either of order h2 of h4 in the spatial grid size h are considered.


Computational Fluid Dynamics Truncation Error Expanded Form Diagonal Dominance Exponential Coefficient 
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Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • S. C. R. Dennis
    • 1
  1. 1.Department of Applied MathematicsUniversity of Western OntarioLondonCanada

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