Volume Penalization Technique for Simulating Acoustic Streaming

We propose a volume penalization method for simulating acoustically actuated flows in geometrically complex microchannels. The fluid response is decomposed using a perturbation approach into two sub-problems: a harmonic first-order system and a time-averaged second-order system. Boundary conditions are enforced by prescribing a zero-structure velocity for the first-order problem and a Stokes drift-based velocity for the second-order problem. The harmonic first-order system is solved using the MUMPS direct solver, while the steady-state second-order system is tackled iteratively with a novel projection-based preconditioner. This preconditioning approach demonstrates strong scalability and effectiveness with respect to increasing penalty force and grid resolution.

We introduce a novel contour integration method for computing the acoustic radiation force on immersed bodies. Tailored for Cartesian grids, this method enhances both accuracy and ease of implementation. We determine optimal penalty parameters and interface widths to ensure accurate solutions. Our results offer the first empirical validation of the volume penalization technique as a viable alternative to body-fitted methods for acoustic streaming simulations. Furthermore, we incorporate the motion of rigid solid particles in acoustically actuated fluids, providing a practical framework for studying the dynamics of immersed objects in acoustofluidic systems.