Inertial coupling for point particle fluctuating hydrodynamics

A method for particle hydrodynamics based on an hybrid Eulerian-Lagrangian approach is presented. Particle dynamics are solved in continuum space while the fluid equations are solved in an Eulerian mesh, and described by finite volume fluctuating hydrodynamics. This set-up is particularly suited for micron-size devices where the Reynolds number is small but thermal fluctuations are important. The particle-fluid coupling force is obtained by imposing zero relative (particle-fluid) velocity at a local average over the particle volume. In doing so the momentum exchanged between fluid and particle is transferred instantaneously ensuring a correct treatment of inertia and correct particle velocity fluctuations uniquely driven by fluid thermal forces. Consistency between the Eulerian and Lagrangian momentum balance is shown to be essential. The scheme is applied to compressible fluids at low Mach number and moderate Reynolds number. A series of tests show that the near velocity field around the particle is correctly captured up to distances of about one particle hydrodynamic diameter. Also, acoustic forces measured under ultrasound waves are in excellent agreement with the theoretical expressions.