Section outline

  • This document reports the Fundamentals of the Finite Difference method (FD) for Computational Fluid Dynamics (CFD) and Numerical Heat Transfer (NHT). In particular, after a general overview of the method and the presentation of the most frequent FD approximations for first and second-order derivatives, it illustrates some different techniques - Taylor series, polynomial interpolation and difference operators - which can be used to derive different schemes for the Finite Difference Equations (FDE) representative of their corresponding Partial Differential Equations (PDE).

    • Fundamentals of the Finite Difference Method File

      An overview of the Finite Difference Method (FDM), one, if not the first, numerical method used in CFD.

      • Introduction
        • Generalities and notation
      • Finite Differences
      • Finite Difference Operators
      • Frequent Finite Difference approximations
      • Compact Finite Difference Schemes
      • Difference representation of Partial Differential Equations
        • Truncation Error
        • Round-Off and Discretization Errors
        • Boundary conditions
        • Application of boundary conditions to 1D unsteady conduction
      • Methods for obtaining Finite Difference equations
        • Taylor series
        • Polynomial fitting
        • Estimation of one-sided boundary derivative
      • Generation of difference formulas by Difference operators
        • Difference formulas for First Derivatives
        • Difference formulas for Higher Order Derivatives