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We present a simple technique for the computation of coarse-scale steady states of dynamical systems with time scale separation in the form of a wrapper around a fine-scale simulator. We discuss how this approach alleviates certain problems encountered by comparable existing approaches, and illustrate its use by computing coarse-scale steady states of a lattice Boltzmann fine scale code. Interestingly, in the same context of multiple time scale problems, the approach can be slightly modified to provide initial conditions (on the slow manifold) with prescribed coarse-scale observables. The approach is based on appropriately designed short bursts of the fine-scale simulator whose results are used to track changes in the coarse variables of interest, a core component of the equation-free framework.
Atmospheric dynamics span a range of time-scales. The projection of measured data to a slow manifold, ${cal M}$, removes fast gravity waves from the initial state for numerical simulations of the atmosphere. We explore further the slow manifold for a
An implicit multiscale method with multiple macroscopic prediction for steady state solutions of gas flow in all flow regimes is presented. The method is based on the finite volume discrete velocity method (DVM) framework. At the cell interface a mul
The mass flow rate of Poiseuille flow of rarefied gas through long ducts of two-dimensional cross-sections with arbitrary shape are critical in the pore-network modeling of gas transport in porous media. In this paper, for the first time, the high-or
The large time and length scales and, not least, the vast number of particles involved in industrial-scale simulations inflate the computational costs of the Discrete Element Method (DEM) excessively. Coarse grain models can help to lower the computa
The linear noise approximation models the random fluctuations from the mean field model of a chemical reaction that unfolds near the thermodynamic limit. Specifically, the fluctuations obey a linear Langevin equation up to order $Omega^{-1/2}$, where