Suchergebnisse

We develop an inertial coupling method for modeling the dynamics of point-like "blob" particles immersed in an incompressible fluid, generalizing previous work for compressible fluids (Balboa Usabiaga et al., 2013). The coupling consistently includes excess (positive or negative) inertia of the particles relative to the displaced fluid, and accounts for thermal fluctuations in the fluid momentum equation. The coupling between the fluid and the blob is based on a no-slip constraint equating the particle velocity with the local average of the fluid velocity, and conserves momentum and energy. We demonstrate that the formulation obeys a fluctuation–dissipation balance, owing to the non-dissipative nature of the no-slip coupling. We develop a spatio-temporal discretization that preserves, as best as possible, these properties of the continuum formulation. In the spatial discretization, the local averaging and spreading operations are accomplished using compact kernels commonly used in immersed boundary methods. We find that the special properties of these kernels allow the blob to provide an effective model of a particle; specifically, the volume, mass, and hydrodynamic properties of the blob are remarkably grid-independent. We develop a second-order semi-implicit temporal integrator that maintains discrete fluctuation–dissipation balance, and is not limited in stability by viscosity. Furthermore, the temporal scheme requires only constant-coefficient Poisson and Helmholtz linear solvers, enabling a very efficient and simple FFT-based implementation on GPUs. We numerically investigate the performance of the method on several standard test problems. In the deterministic setting, we find the blob to be a remarkably robust approximation to a rigid sphere, at both low and high Reynolds numbers. In the stochastic setting, we study in detail the short and long-time behavior of the velocity autocorrelation function and observe agreement with all of the known behavior for rigid sphere immersed in a fluctuating fluid. The proposed inertial coupling method provides a low-cost coarse-grained (minimal resolution) model of particulate flows over a wide range of time-scales ranging from Brownian to convection-driven motion ; A. Donev was supported in part by the Air Force Office of Scientific Research under grant number FA9550-12-1-0356. B. Griffith acknowledges research support from the National Science Foundation un-der awards OCI 1047734 and DMS 1016554. R. Delgado-Buscalioni and F. Balboa acknowledge funding from the Spanish government FIS2010-22047-C05 and from the Comunidad de Madrid MODELICO-CM (S2009/ESP-1691). Collaboration between A. Donev and R. Delgado-Buscalioni was fostered at the Kavli Institute for Theoretical Physics in Santa Barbara, California, and supported in part by the National Science Foundation under Grant No. NSF PHY05-51164

We develop numerical schemes for solving the isothermal compressible and incompressible equations of fluctuating hydrodynamics on a grid with staggered momenta. We develop a second-order accurate spatial discretization of the diffusive, advective, and stochastic fluxes that satisfies a discrete fluctuation-dissipation balance and construct temporal discretizations that are at least second-order accurate in time deterministically and in a weak sense. Specifically, the methods reproduce the correct equilibrium covariances of the fluctuating fields to the third (compressible) and second (incompressible) orders in the time step, as we verify numerically. We apply our techniques to model recent experimental measurements of giant fluctuations in diffusively mixing fluids in a microgravity environment [A. Vailati et al., Nat. Comm., 2 (2011), 290]. Numerical results for the static spectrum of nonequilibrium concentration fluctuations are in excellent agreement between the compressible and incompressible simulations and in good agreement with experimental results for all measured wavenumbers ; These authors' research was supported by the Spanish government FIS2010-22047-C0S and the Comunidad de Madrid MODELICO-CM (S2009/ESP-1691). This author's research was supported by the DOE Applied Mathematics Program of the DOE Office of Advanced Scientific Computing Research under the U.S. Department of Energy under contract DE-AC02-05CH11231. The fourth author's research was supported by the DOE Applied Mathematics Program of the DOE Office of Advanced Scientific Computing Research under the U.S. Department of Energy under contract DE-AC02-05CH11231 and by the National Science Foundation under grant DMS-1115341. The fifth author's research was supported by the DOE Computational Science Graduate Fellowship under grant DE-FG02-97ER25308. This author's research was supported by the National Science Foundation under awards OCI 1047734 and DMS 1016554.