# Coarse-Grained Hydrodynamics from Correlation Functions

## Abstract

This paper will describe a formalism for using correlation functions between different grid cells as the basis for determining coarse-grained hydrodynamic equations for modeling the behavior of mesoscopic fluid systems. Configurations from a molecular dynamics simulation or other atomistic simulation are projected onto basis functions representing grid cells in a continuum hydrodynamic simulation. Equilibrium correlation functions between different grid cells are evaluated from the molecular simulation and used to determine the evolution operator for the coarse-grained hydrodynamic system. The formalism is demonstrated on a discrete particle simulation of diffusion with a spatially dependent diffusion coefficient. Correlation functions are calculated from the particle simulation and the spatially varying diffusion coefficient is recovered using a fitting procedure.

- Authors:

- BATTELLE (PACIFIC NW LAB)

- Publication Date:

- Research Org.:
- Pacific Northwest National Lab. (PNNL), Richland, WA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1511269

- Report Number(s):
- PNNL-SA-127413

- DOE Contract Number:
- AC05-76RL01830

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. E, Statistical, Nonlinear, Biological, and Soft Matter Physics

- Additional Journal Information:
- Journal Volume: 97; Journal Issue: 2

- Country of Publication:
- United States

- Language:
- English

- Subject:
- HPC

### Citation Formats

```
Palmer, Bruce J.
```*Coarse-Grained Hydrodynamics from Correlation Functions*. United States: N. p., 2018.
Web. doi:10.1103/PhysRevE.97.022106.

```
Palmer, Bruce J.
```*Coarse-Grained Hydrodynamics from Correlation Functions*. United States. doi:10.1103/PhysRevE.97.022106.

```
Palmer, Bruce J. Tue .
"Coarse-Grained Hydrodynamics from Correlation Functions". United States. doi:10.1103/PhysRevE.97.022106.
```

```
@article{osti_1511269,
```

title = {Coarse-Grained Hydrodynamics from Correlation Functions},

author = {Palmer, Bruce J.},

abstractNote = {This paper will describe a formalism for using correlation functions between different grid cells as the basis for determining coarse-grained hydrodynamic equations for modeling the behavior of mesoscopic fluid systems. Configurations from a molecular dynamics simulation or other atomistic simulation are projected onto basis functions representing grid cells in a continuum hydrodynamic simulation. Equilibrium correlation functions between different grid cells are evaluated from the molecular simulation and used to determine the evolution operator for the coarse-grained hydrodynamic system. The formalism is demonstrated on a discrete particle simulation of diffusion with a spatially dependent diffusion coefficient. Correlation functions are calculated from the particle simulation and the spatially varying diffusion coefficient is recovered using a fitting procedure.},

doi = {10.1103/PhysRevE.97.022106},

journal = {Physical Review. E, Statistical, Nonlinear, Biological, and Soft Matter Physics},

number = 2,

volume = 97,

place = {United States},

year = {2018},

month = {2}

}