# Three-dimensional Hybrid Continuum-Atomistic Simulations for Multiscale Hydrodynamics

## Abstract

We present an adaptive mesh and algorithmic refinement (AMAR) scheme for modeling multi-scale hydrodynamics. The AMAR approach extends standard conservative adaptive mesh refinement (AMR) algorithms by providing a robust flux-based method for coupling an atomistic fluid representation to a continuum model. The atomistic model is applied locally in regions where the continuum description is invalid or inaccurate, such as near strong flow gradients and at fluid interfaces, or when the continuum grid is refined to the molecular scale. The need for such ''hybrid'' methods arises from the fact that hydrodynamics modeled by continuum representations are often under-resolved or inaccurate while solutions generated using molecular resolution globally are not feasible. In the implementation described herein, Direct Simulation Monte Carlo (DSMC) provides an atomistic description of the flow and the compressible two-fluid Euler equations serve as our continuum-scale model. The AMR methodology provides local grid refinement while the algorithm refinement feature allows the transition to DSMC where needed. The continuum and atomistic representations are coupled by matching fluxes at the continuum-atomistic interfaces and by proper averaging and interpolation of data between scales. Our AMAR application code is implemented in C++ and is built upon the SAMRAI (Structured Adaptive Mesh Refinement Application Infrastructure)more »

- Authors:

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 15014093

- Report Number(s):
- UCRL-JRNL-203681

Journal ID: ISSN 0098-2202; JFEGA4; TRN: US200803%%686

- DOE Contract Number:
- W-7405-ENG-48

- Resource Type:
- Journal Article

- Journal Name:
- Published in: Journal of Fluids Engineering, vol. 126, n/a, September 1, 2004, pp. 768-777

- Additional Journal Information:
- Journal Volume: 126; Journal ID: ISSN 0098-2202

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUMM MECHANICS, GENERAL PHYSICS; ALGORITHMS; HYDRODYNAMICS; IMPLEMENTATION; INTERPOLATION; LAWRENCE LIVERMORE NATIONAL LABORATORY; RESOLUTION; SIMULATION

### Citation Formats

```
Wijesinghe, S, Hornung, R, Garcia, A, and Hadjiconstantinou, N.
```*Three-dimensional Hybrid Continuum-Atomistic Simulations for Multiscale Hydrodynamics*. United States: N. p., 2004.
Web. doi:10.1115/1.1792275.

```
Wijesinghe, S, Hornung, R, Garcia, A, & Hadjiconstantinou, N.
```*Three-dimensional Hybrid Continuum-Atomistic Simulations for Multiscale Hydrodynamics*. United States. doi:10.1115/1.1792275.

```
Wijesinghe, S, Hornung, R, Garcia, A, and Hadjiconstantinou, N. Thu .
"Three-dimensional Hybrid Continuum-Atomistic Simulations for Multiscale Hydrodynamics". United States. doi:10.1115/1.1792275. https://www.osti.gov/servlets/purl/15014093.
```

```
@article{osti_15014093,
```

title = {Three-dimensional Hybrid Continuum-Atomistic Simulations for Multiscale Hydrodynamics},

author = {Wijesinghe, S and Hornung, R and Garcia, A and Hadjiconstantinou, N},

abstractNote = {We present an adaptive mesh and algorithmic refinement (AMAR) scheme for modeling multi-scale hydrodynamics. The AMAR approach extends standard conservative adaptive mesh refinement (AMR) algorithms by providing a robust flux-based method for coupling an atomistic fluid representation to a continuum model. The atomistic model is applied locally in regions where the continuum description is invalid or inaccurate, such as near strong flow gradients and at fluid interfaces, or when the continuum grid is refined to the molecular scale. The need for such ''hybrid'' methods arises from the fact that hydrodynamics modeled by continuum representations are often under-resolved or inaccurate while solutions generated using molecular resolution globally are not feasible. In the implementation described herein, Direct Simulation Monte Carlo (DSMC) provides an atomistic description of the flow and the compressible two-fluid Euler equations serve as our continuum-scale model. The AMR methodology provides local grid refinement while the algorithm refinement feature allows the transition to DSMC where needed. The continuum and atomistic representations are coupled by matching fluxes at the continuum-atomistic interfaces and by proper averaging and interpolation of data between scales. Our AMAR application code is implemented in C++ and is built upon the SAMRAI (Structured Adaptive Mesh Refinement Application Infrastructure) framework developed at Lawrence Livermore National Laboratory. SAMRAI provides the parallel adaptive gridding algorithm and enables the coupling between the continuum and atomistic methods.},

doi = {10.1115/1.1792275},

journal = {Published in: Journal of Fluids Engineering, vol. 126, n/a, September 1, 2004, pp. 768-777},

issn = {0098-2202},

number = ,

volume = 126,

place = {United States},

year = {2004},

month = {4}

}

Works referenced in this record:

##
Breakdown of translational and rotational equilibrium in gaseous expansions

journal, November 1970

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- AIAA Journal, Vol. 8, Issue 11