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In this work, we propose and test a method for calculating Stokes dragapplicable to particle-laden fluid flows where two-way momentum coupling isimportant. In the point-particle formulation, particle dynamics are coupled tofluid dynamics via a source term that appears in the respective momentumequations. When the particle Reynolds number is small and the particle diameteris smaller than the fluid scales, it is common to approximate the momentumcoupling source term as the Stokes drag. The Stokes drag force depends on thedifference between the undisturbed fluid velocity evaluated at the particlelocation, and the particle velocity. However, owing to two-way coupling, thefluid velocity is modified in the neighborhood of a particle, relative to itsundisturbed value. This causes the computed Stokes drag force to beunderestimated in two-way coupled point-particle simulations. We developestimates for the drag force error as function of the particle size relative tothe grid size. We then develop a correction method that estimates theundisturbed fluid velocity from the computed disturbed velocity field. Thecorrection scheme is tested for a particle settling in an otherwise quiescentfluid and is found to reduce the error in computed settling velocity by anorder of magnitude compared with common interpolation schemes.

Accurate calculation of Stokes drag for point-particle tracking in two-way coupled flows