Calculation Verification: Pointwise Estimation of Solutions and Their Method-Associated Numerical Error

Code Verification of the HIGRAD Computational Fluid Dynamics Solver

“…The refinement ratio of equation 16is, by definition, always greater than one since ∆x C ≥ ∆x F . The procedure outlined in equations (12)(13)(14)(15)(16) indicates that two calculations with different levels of mesh resolution are sufficient to estimate the rate-of-convergence p. If additional runs are available, then a least-squares solver can easily be implemented to estimate the pair of parameters (p; β) that best-fits the model of truncation error of equation (9).…”

“…The main difference is that equation 17depends on a triplet of unknown parameters (y Reference ; p; ), hence, requiring a minimum of three code runs. The reader is referred to References [15] and [16] for detailed discussions of how to handle the case of non-monotonic convergence in a manner similar to the derivations that follow.…”