A non-iterative immersed boundary method for spherical particles of arbitrary density ratio

Abstract

In this paper an immersed boundary method with semi-implicit fluid–solid coupling for mobile particles of arbitrary density ratio is developed. The new scheme does not require any iterations to balance fluid forces and particle forces at the interface. A new formulation of the particle equations of motion is proposed which not only accounts for the particle itself but also for a Lagrangian layer surrounding the particle surface. Furthermore, it is shown by analytical considerations that the six equations for the linear and angular velocity of the spherical particle decouple which allows their sequential solution. On this basis a new time integration scheme is obtained which is unconditionally stable for all fluid–solid density ratios and enables large time steps, with Courant numbers around unity. The new scheme is extensively validated for various test cases and its convergence is assessed. An appealing issue is that compared to existing immersed boundary methods the new scheme only alters coefficients in the particle equations and the order of the steps, making it easy to implement in present codes with explicit coupling. This substantially extends the field of application of such methods.