Evolution of an Incompressible Fluid Drop Under a Central Force Field: Analytical Benchmark Solutions for Free‐Surface Flows

We present a set of exact and approximate analytical solutions describing the evolution of a fluid drop under the action of a central force field, in both two and three dimensions. The fluid is assumed to be Newtonian and incompressible with a free surface and no solid boundaries The absence of solid walls eliminates boundary‐layer effects, enabling focused analysis of free‐surface dynamics. The benchmarks address key phenomena: nonlinear surface deformation, viscous damping and vorticity, and small‐amplitude oscillations under viscosity and surface tension. Designed for minimal complexity and straightforward implementation, these cases provide rigorous conditions for evaluating the accuracy and stability of numerical solvers, supporting reliable computational fluid dynamics validation and fundamental studies of free‐surface flows.