Differential-equation-based representation of truncation errors for accurate numerical simulation
Abstract
High-order compact finite difference schemes for 2D convection-diffusion-type differential equations with constant and variable convection coefficients are derived. The governing equations are employed to represent leading truncation terms, including cross-derivatives, making the overall O(h super 4) schemes conform to a 3 x 3 stencil. It is shown that the two-dimensional constant coefficient scheme collapses to the optimal scheme for the one-dimensional case wherein the finite difference equation yields nodally exact results. The two-dimensional schemes are tested against standard model problems, including a Navier-Stokes application. Results show that the two schemes are generally more accurate, on comparable grids, than O(h super 2) centered differencing and commonly used O(h) and O(h super 3) upwinding schemes.
- Publication:
-
International Journal for Numerical Methods in Fluids
- Pub Date:
- September 1991
- DOI:
- 10.1002/fld.1650130606
- Bibcode:
- 1991IJNMF..13..739M
- Keywords:
-
- Computational Fluid Dynamics;
- Convection-Diffusion Equation;
- Differential Equations;
- Finite Difference Theory;
- Truncation Errors;
- Digital Simulation;
- Navier-Stokes Equation;
- Partial Differential Equations;
- Reynolds Number;
- Fluid Mechanics and Heat Transfer