Suchergebnisse

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.