A Eulerian-Lagrangian Method Applied to Fluid Flow in Lid-Driven Cavities With Irregular Bottom Walls

Abstract

In this work, a mixed Eulerian-Lagrangian method is employed to explore fluid flows in two-dimensional, lid-driven, irregular-bottom cavities. The methodology can handle fluid flows in the presence of irregularly shaped solid boundaries. A fixed Cartesian grid is used in the discretization of the momentum and mass equations, precluding the need to generate a grid to accommodate the non-Cartesian walls. Special treatment is required to deal with the control volumes located at the fluid–solid interface, an approach that is described herein. The discretization of the governing equations uses the finite-volume method with a collocated, i.e., cell-centered arrangement of velocity and pressure. The procedure is verified by solving two-dimensional lid-driven cavity flows for different Reynolds numbers in standard cavity shapes such as semicircular, rectangular, and square, with or without an irregular bottom wall. Results for the velocity components along the geometric centerline, stream function patterns, and pressure contours are presented and discussed. Excellent congruence with benchmark solutions is obtained.