Estimation of the spatial discretization error in numerical simulations of bubbly flows

Abstract

Abstract Accurate spatial discretization error estimates are essential for some CFD applications. Notwithstanding, this subject has been systematically disregarded in the literature on bubbly flow simulation. This work evaluated the suitability of three error estimators (EEMs) in simulations of a benchmark bubble column. The employed EEMs were: Direct Taylor series (DTS), Richardson Extrapolation (RExt), and Eca-Hoekstra Least-Squares (EH-LS). The modeling approaches for the bubbly flow were: standard two-fluid model (TFM), hyperbolic TFM (hTFM), and mixture model (MixtM). Geometric means of the estimated error and of the difference between the solution obtained with the considered mesh and a nearly mesh-independent solution were used as comparison metrics. DTS resulted in inaccurate estimates for coarse meshes. Both EH-LS and RExt generated accurate results for MixtM, the latter presenting lower computational cost. RExt could not deal adequately with the oscillatory convergence pattern of hTFM. EH-LS was the only method suitable for both MixtM and hTFM.