An approach for both the computation of coarse-scale steady state solutions and initialization on a slow manifold

TL;DR

This paper introduces a simple wrapper technique around fine-scale simulators to compute coarse-scale steady states and initialize on slow manifolds, addressing challenges in multiscale dynamical systems.

Contribution

It presents a novel, straightforward method for computing steady states and initial conditions on slow manifolds using short bursts of fine-scale simulations within the equation-free framework.

Findings

Successfully computes coarse steady states of lattice Boltzmann models.

Provides initial conditions on slow manifolds with prescribed coarse observables.

Alleviates problems faced by existing multiscale simulation approaches.

Abstract

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.