Spatially Adaptive Stochastic Multigrid Methods for Fluid-Structure Systems with Thermal Fluctuations

TL;DR

This paper introduces a stochastic multigrid method for simulating fluid-structure interactions at microscopic scales, efficiently capturing hydrodynamics and thermal fluctuations with adaptive meshes and O(N log(N)) complexity.

Contribution

It develops a novel spatially adaptive stochastic multigrid approach for fluid-structure systems with thermal fluctuations, improving efficiency and accuracy.

Findings

Efficient computation of hydrodynamic interactions with thermal fluctuations.

Supports spatially adaptive meshes for better resolution.

Achieves computational complexity of O(N log(N)).

Abstract

In microscopic mechanical systems interactions between elastic structures are often mediated by the hydrodynamics of a solvent fluid. At microscopic scales the elastic structures are also subject to thermal fluctuations. Stochastic numerical methods are developed based on multigrid which allow for the efficient computation of both the hydrodynamic interactions in the presence of walls and the thermal fluctuations. The presented stochastic multigrid approach provides efficient real-space numerical methods for generating the required stochastic driving fields with long-range correlations consistent with statistical mechanics. The presented approach also allows for the use of spatially adaptive meshes in resolving the hydrodynamic interactions. Numerical results are presented which show the methods perform in practice with a computational complexity of O(N log(N)).