Accuracy of finitedifference methods in recirculating flows
Abstract
The accuracy of six numerical approximations of the convection terms in the conservation equations is examined for a steady, recirculating flow. Quadratic upwind, central, ninepoint, thirdorder, and powerlaw approximations are tested as alternatives to the widely used upwind/central hybrid method. Forced flow in a heated cavity is chosen as a reasonably severe test problem. An exact analytical solution is used to evaluate truncation errors and solution errors. Expressions for the leading truncated terms, including velocity derivatives, provide insight into why errors in the convection terms dominate errors in the diffusion terms for high grid Peclet numbers. If an average solution error of less than 10 percent is desired, higher order methods are clearly superior to the firstorder upwind/hybrid method. One must have at least one finite domain within a wall gradient layer to reduce flux errors to 10 percent with the secondoder centraldifference method, whereas one must have at least two finite domains across the layer to achieve similar accuracy with the firstorder hybrid method. Both quadratic upwind and central differencing are recommended for the numerical approximation of the convection terms.
 Publication:

Numerical Heat Transfer
 Pub Date:
 September 1983
 Bibcode:
 1983NumHT...6..283B
 Keywords:

 Computational Fluid Dynamics;
 Convective Flow;
 Finite Difference Theory;
 Recirculative Fluid Flow;
 Steady Flow;
 Accuracy;
 Approximation;
 Cavities;
 Conservation Equations;
 Error Analysis;
 Truncation Errors;
 Fluid Mechanics and Heat Transfer