A Verification And Validation Exercise For The Flow Over A Backward Facing Step

This paper presents Solution Verification and Validation exercises for the flow over a backward facing step. Two completely different flow solvers are applied: ReFRESCO, using a finite-volume discretization of the momentum equations in strong conservation form and a pressure-correction algorithm based on the SIMPLE approach; PARNASSOS, discretizing the non-conservative continuity and momentum equations written in Contravariant form with finite-differences. Two sets of geometrically similar singleblock structured grids are selected to perform Solution Verification. A procedure based on a least squares version of the Grid Convergence Index is used to estimate the numerical uncertainty of functional and local flow quantities. The iterative error is evaluated for the ReFRESCO calculations by comparing solutions obtained with less demanding convergence criteria to flow fields converged to machine accuracy. As already experienced in similar exercises with PARNASSOS, the iterative error may be 2 to 3 orders of magnitude larger than the L∞ norm of normalized residuals and/or flow variable changes between consecutive iterations at the last iteration performed. Furthermore, the iterative errors must be two orders of magnitude smaller than the discretization error to have a negligible influence on the determination of the latter. The present Solution Verification exercise confirms that misleading conclusions may be drawn from numerical simulations without the knowledge of the numerical uncertainty. An example of the application of the ASME V&V-20 Validation procedure is presented for an horizontal velocity profile downstream of the step. It is clear that the proposed procedure is a step forward compared to the simple graphical comparisons between numerical predictions and experimental data.