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This paper describes the extension of a
recently developed numerical solver for the Landau-Lifshitz
Navier-Stokes (LLNS) equations to binary mixtures in three
dimensions. The LLNS equations incorporate thermal fluctuations into
macroscopic hydrodynamics by using white-noise fluxes. These
stochastic PDEs are more complicated in three dimensions due to the
tensorial form of the correlations for the stochastic fluxes and in
mixtures due to couplings of energy and concentration fluxes (e.g.,
Soret...
This paper analyzes the random fluctuations obtained by a heterogeneous multi-scale first-order finite element method applied to solve elliptic equations with a random potential. Several multi-scale numerical algorithms have been shown to correctly capture the homogenized limit of solutions of elliptic equations with coefficients modeled as stationary and ergodic random fields. Because theoretical results are available in the continuum setting for such equations, we consider here the case of a second-order...
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