<p>We present a methodology for simulating dilute suspensions of particles settling under gravity, with the main purpose of overcoming limitations of triply periodic configurations, mainly the strong vertical correlation that hinders the study of cluster dynamics. The current approach removes vertical periodicity and employs a moving reference frame, enabling efficient simulations of both single- and many-particle cases. We illustrate the method with two examples of increasing complexity: a single particle in the steady vertical regime and a many-particle case at a parametric point where collective effects were previously observed and recovered here. A converged, free-of-corrections time interval of approximately <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(600\,D/U_g\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>600</mn> <mspace width="0.166667em" /> <mi>D</mi> <mo stretchy="false">/</mo> <msub> <mi>U</mi> <mi>g</mi> </msub> </mrow> </math></EquationSource> </InlineEquation> is simulated in the many-particle case, representing the first simulation of this kind to date. New physical insights can be explored thanks to this new configuration, for example, the effect of still fluid on the first layer of particles encountered by the fluid, or the turbulent character of the flow after a swarm of particles has passed by. Finally, the method only requires parameter tuning, allowing implementation within existing solvers without changes to their core formulation: for a standard configuration with an imposed free stream velocity at the inlet, only the input velocity (or the viscosity of the fluid) and the time step need to be updated.</p>