Quantifying the fluid modeling capability of SPH and CLE through the study of the LID-driven cavity problem

Despite recent interest in complex fluid-structure interaction problems, the baseline fluid modeling capability for commercially available numerical methodologies used for multidisciplinary analysis is yet to be established. The current work is among those to first underline such a reference for coupled Lagrangian-Eulerian (CLE) and smooth particle hydrodynamics (SPH). These methodologies are quantitatively assessed using the classical 2-D lid-driven cavity and compared against an implicit Navier-Stokes solution in addition to other benchmarks from the literature. Qualitative comparison is made through the use of velocity magnitude contour plots with accompanying streamlines, whereas quantitative analysis is made using centerline velocity profiles for both U and V flows. Throughout the investigated Reynolds numbers (1000-20, 000), SPH provides inaccurate results and is unable to represent vorticity in the cavity corners. Alternatively, CLE retains a high level of accuracy up to Re = 10, 000, before deviating from published literature at Re = 20, 000. In addition to being qualitatively similar, the centerline profiles consistently display ≤ 10% error when compared to the Navier-Stokes solutions. By establishing the limits of closed-system fluid modeling capability for SPH and CLE, this work can be extended to full fluid-scenarios.