# A stochastic immersed boundary method for fluid-structure dynamics at microscopic length scales

@article{Atzberger2007ASI, title={A stochastic immersed boundary method for fluid-structure dynamics at microscopic length scales}, author={Paul J. Atzberger and Peter R. Kramer and Charles S. Peskin}, journal={J. Comput. Phys.}, year={2007}, volume={224}, pages={1255-1292} }

In modeling many biological systems, it is important to take into account flexible structures which interact with a fluid. At the length scale of cells and cell organelles, thermal fluctuations of the aqueous environment become significant. In this work, it is shown how the immersed boundary method of C.S. Peskin, The immersed boundary method, Acta Num. 11 (2002) 1-39.] for modeling flexible structures immersed in a fluid can be extended to include thermal fluctuations. A stochastic numerical…

## Figures, Tables, and Topics from this paper

## 154 Citations

Error analysis of a stochastic immersed boundary method incorporating thermal fluctuations

- Mathematics, Computer ScienceMath. Comput. Simul.
- 2008

A stochastic numerical scheme for an extended immersed boundary method which incorporates thermal fluctuations for the simulation of microscopic biological systems consisting of fluid and immersed…

Stochastic immersed boundary method incorporating thermal fluctuations

- Physics
- 2007

We give a brief introduction to the stochastic immersed boundary method which allows for simulation of small length-scale physical systems in which elastic structures interact with a fluid flow in…

SIMULATION OF COMPLEX FLUIDS AND SOFT MATERIALS USING STOCHASTIC EULERIAN LAGRANGIAN METHODS WITH SHEAR BOUNDARY CONDITIONS

- 2010

We introduce computational methods for rheological studies of soft materials and complex fluids. The approach allows for investigations of the roles played by the microstructure interactions and…

Fluctuating hydrodynamic methods for fluid-structure interactions in confined channel geometries

- Physics
- 2017

We develop computational methods for the study of fluid-structure interactions subject to thermal fluctuations when confined within channels with slit-like geometry. The methods take into account the…

An immersed boundary method based on the lattice Boltzmann approach in three dimensions, with application

- Mathematics, Computer ScienceComput. Math. Appl.
- 2011

A 3D lattice Boltzmann model (D3Q19) is used within the immersed boundary method to simulate a viscous flow past a flexible sheet tethered at its middle line in a 3D channel and determine a drag scaling law for the sheet.

Title Fluctuating hydrodynamic methods for fluid-structure interactions in confined channel geometries Permalink

- 2018

We develop computational methods for the study of fluid-structure interactions subject to thermal fluctuations when confined within channels with slit-like geometry. The methods take into account the…

Efficient simulation of thermally fluctuating biopolymers immersed in fluids on 1-micron, 1-second scales

- Physics, Computer ScienceJ. Comput. Phys.
- 2019

An efficient scheme based on the stochastic immersed boundary method, Stokeslets, and multiple timestepping is developed and it is suggested that this method will reveal significant hydrodynamic effects in biological phenomena.

Finite element formulation of fluctuating hydrodynamics for fluids filled with rigid particles using boundary fitted meshes

- Computer Science, MathematicsJ. Comput. Phys.
- 2016

A finite element implementation of fluctuating hydrodynamics with a moving boundary fitted mesh for treating the suspended particles fulfills the fluctuation-dissipation theorem exactly at the discrete level.

The immersed molecular finite element method

- Physics
- 2012

Abstract In this paper, we present the framework of the immersed molecular finite element method (IMFEM). The framework incorporates Brownian motion dynamics, a molecular phenomenon predominantly…

Fluid-particle dynamics for passive tracers advected by a thermally fluctuating viscoelastic medium

- Physics, Computer ScienceJ. Comput. Phys.
- 2017

This work proposes a viscoelastic generalization of the LandauLifschitz NavierStokes fluid model, and investigates the properties of particles that are passively advected by such a medium, exploiting certain exact formulations that arise from the Gaussian nature of the fluid model and introducing analysis of memory in the fluid statistics.

## References

SHOWING 1-10 OF 112 REFERENCES

Error analysis of a stochastic immersed boundary method incorporating thermal fluctuations

- Mathematics, Computer ScienceMath. Comput. Simul.
- 2008

A stochastic numerical scheme for an extended immersed boundary method which incorporates thermal fluctuations for the simulation of microscopic biological systems consisting of fluid and immersed…

Stochastic Mode Reduction for the Immersed Boundary Method

- Mathematics, Computer ScienceSIAM J. Appl. Math.
- 2004

It is found, in the limit of small Reynolds (or Kubo) number, that the Lagrangian particle constituents of the immersed structures undergo a drift-diffusive motion with several physically correct featur...

NUMERICAL SIMULATIONS OF PARTICULATE SUSPENSIONS VIA A DISCRETIZED BOLTZMANN EQUATION: PART 1. THEORETICAL FOUNDATION

- Physics
- 1993

A new and very general technique for simulating solid-fluid suspensions is described ; its most important feature is that the computational cost scales linearly with the number of particles. The…

Dynamic simulation of sheared suspensions. I. General method

- Chemistry
- 1984

A general method is presented for simulating the dynamical behavior of a suspension of particles which interact through both hydrodynamic and nonhydrodynamic forces. In the molecular-dynamics-like…

Accelerated Stokesian Dynamics simulations

A new implementation of the conventional Stokesian Dynamics (SD) algorithm, called accelerated Stokesian Dynamics (ASD), is presented. The equations governing the motion of N particles suspended in a…

Incorporating thermal fluctuations into the immersed boundary method

- Physics
- 2003

We present a new computational method for simulating microscopic processes in physiology which accounts for stochastic thermal fluctuations and a dynamically evolving fluid environment. This latter…

The immersed boundary method

- MathematicsActa Numerica
- 2002

This paper is concerned with the mathematical structure of the immersed boundary (IB) method, which is intended for the computer simulation of fluid–structure interaction, especially in biological…

STOKESIAN DYNAMICS

- 2006

Particles suspended or dispersed in a fluid medium occur in a wide variety of natural and man-made s ttings, e.g. slurries, composite materials, ceramics, colloids, polymers, proteins, etc. The…

Velocity correlations of a thermally fluctuating brownian particle : A novel model of the hydrodynamic coupling

- Physics
- 2006

Abstract A new derivation of the velocity correlations of a thermally fluctuating Brownian particle is shown by direct calculation from a stochastic hydrodynamic model in which the fluid-particle…

DISSIPATIVE PARTICLE DYNAMICS : BRIDGING THE GAP BETWEEN ATOMISTIC AND MESOSCOPIC SIMULATION

- Chemistry
- 1997

We critically review dissipative particle dynamics (DPD) as a mesoscopic simulation method. We have established useful parameter ranges for simulations, and have made a link between these parameters…