A temporal discretization scheme to compute the motion of light particles in viscous flows by an immersed boundary method

The paper introduces a time scheme for an immersed boundary method which enables the efficient, phase-resolving simulation of very light particles in viscous flow. A simple modification of the time scheme of the method detailed in Kempe and Fröhlich (2012) [34] is proposed to extend the range of applicability to particle-to-fluid density ratios as they occur with bubbles in liquids. This modification is termed 'virtual mass approach'. It is shown for the generic test case of a sphere moving under Stokes flow conditions that the approach can be used in conjunction with several time integration schemes without altering the order of convergence of the base scheme. The new scheme is rigorously validated for the three-dimensional case of a sphere rising or settling at finite Reynolds number, as well as for the rotation of a sphere in viscous flow.