A Boundary Integral Method for Compressible Stokes Flow

A recently developed type of biochip employs ultrasonic surface acoustic waves (SAWs) as a microscale pumping and mixing mechanism for fluids. The driving force for fluid flow is an effect of nonlinear acoustics known as acoustic streaming. We recently studied a two–scale numerical model to describe this effect, which was discretized using classical finite element methods. The micro–scale part of the model describes the propagation of damped acoustic waves. Since the used equations are linear and homogeneous, it is natural to look toward a boundary integral method and attempt a coupling with the FEM scheme still employed in the macro–scale model part. One main ingredient for this approach, namely explicit formulas for free–space Green's functions describing damped acoustics, appear to be novel. We will describe some details of the new scheme, which shows a promising gain of efficiency compared to using FEM for damped acoustics.