Computation of the Basset force: recent advances and environmental flow applications

Abstract

When numerically integrating the equation describing the motion of a particle in a carrier fluid, the computation of the Basset (history) force becomes by far the most expensive and cumbersome, as opposed to forces such as drag, virtual mass, lift, buoyancy and Magnus. The expression representing the Basset force constitutes an integro-differential term whose standard integrand is singular when the upper integration limit is enforced. These shortcomings have led some researchers to either disregard or outright neglect the contribution of the Basset force to the total force, even in those cases where it may yield to important errors in the determination of particle trajectories in the computation of sediment transport and other environmental flows. This work is devoted to review four recent contributions associated with the computation of the Basset force, and to compare their proposals to diminish the inherent problems of the term integration. All papers, except one, use variants of a window-based approach; the most recent contribution, in turn, employs a specialized quadrature to increase the accuracy of the computation. An analysis was carried out to compare CPU computation times, rates of convergence and accuracy of the approximations versus a known analytical solution. All methods provide sound solutions to the issues associated with the computation of the Basset force; further, a road map to select the best solution for each given problem is provided. Finally, we discuss the implications of the techniques for the simulation of sediment transport processes and other environmental flows.

Long-time persistence of hydrodynamic memory boosts microparticle transport

“…(1)] is challenging to solve numerically due to complications arising from the integral and, in the finite-temperature case, time-correlations in thermal fluctuations that give rise to colored noise [14]:…”

“…The memoryless assumption, however, tacitly implies that τ ν τ B ; these timescales are not well separated in dense media (e.g., liquids), even when Re 1 [11][12][13]. This is indeed the case for the myriad mesoscopic phenomena at the micron scale and below, such as conformational changes in biomacromolecules [14,15], unsteady motion of microswimmers [16,17], colloidal flows [4,18], and particle dispersion and sedimentation in turbulence or environmental flows [19]. Yet, without a clear picture of the physical mechanism, a frugal modeler may still reason that memory effects can be safely ignored if relevant observation timescales, such as long-time steady-state behavior, are much longer than both τ ν and τ B .…”

Enhanced settling of nonheavy inertial particles in homogeneous isotropic turbulence: The role of the pressure gradient and the Basset history force

“…Improving the accuracy of the numerical calculation of the Basset history force has been an active field of research in the last decade [13,14,35,36]. A recent review paper [15] concludes that the method by Van Hinsberg et al [13] gives the best balance between computing time and accuracy.…”

“…The implementation of these forces makes the calculation more complex and computationally more expensive. Advances in hardware computing power and algorithm efficiency make the additional computational cost associated with the evaluation of these forces (and particle trajectories derived from them) more acceptable compared to a decade ago [13][14][15]. Another subtlety is related with the particle size compared to the Kolmogorov length scale η (or the dissipation scale) of the turbulent flow.…”

Bed particle saltation in turbulent wall-shear flow: a review

“…Over recent decades, momentous advances in the mechanics of bed particle saltation have been primarily made through experimental observations [2,3,7,8,. In addition, several analytical and numerical studies have been carried out to model bed particle saltation [46][47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62]. Before going into the details of the salient features of bed particle saltation, it is rather interesting to throw some light on the threshold of bed particle saltation.…”