# Numerical solution of plasma fluid equations using locally refined grids

## Abstract

This paper describes a numerical method for the solution of plasma fluid equations on block-structured, locally refined grids. The plasma under consideration is typical of those used for the processing of semiconductors. The governing equations consist of a drift-diffusion model of the electrons and an isothermal model of the ions coupled by Poisson's equation. A discretization of the equations is given for a uniform spatial grid, and a time-split integration scheme is developed. The algorithm is then extended to accommodate locally refined grids. This extension involves the advancement of the discrete system on a hierarchy of levels, each of which represents a degree of refinement, together with synchronization steps to ensure consistency across levels. A brief discussion of a software implementation is followed by a presentation of numerical results.

- Authors:

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab., Livermore, CA (US)

- Sponsoring Org.:
- USDOE Office of Defense Programs (DP) (US)

- OSTI Identifier:
- 16136

- Report Number(s):
- UCRL-ID-126401

ON: DE97053435; TRN: US200432%%301

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

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: Supercedes report DE97053435; PBD: 26 Jan 1997

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING; 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ALGORITHMS; ELECTRONS; IMPLEMENTATION; PLASMA; PROCESSING; SYNCHRONIZATION; NUMERICAL SOLUTION; PLASMA FLUID EQUATIONS

### Citation Formats

```
Colella, P., LLNL.
```*Numerical solution of plasma fluid equations using locally refined grids*. United States: N. p., 1997.
Web. doi:10.2172/16136.

```
Colella, P., LLNL.
```*Numerical solution of plasma fluid equations using locally refined grids*. United States. doi:10.2172/16136.

```
Colella, P., LLNL. Sun .
"Numerical solution of plasma fluid equations using locally refined grids". United States. doi:10.2172/16136. https://www.osti.gov/servlets/purl/16136.
```

```
@article{osti_16136,
```

title = {Numerical solution of plasma fluid equations using locally refined grids},

author = {Colella, P., LLNL},

abstractNote = {This paper describes a numerical method for the solution of plasma fluid equations on block-structured, locally refined grids. The plasma under consideration is typical of those used for the processing of semiconductors. The governing equations consist of a drift-diffusion model of the electrons and an isothermal model of the ions coupled by Poisson's equation. A discretization of the equations is given for a uniform spatial grid, and a time-split integration scheme is developed. The algorithm is then extended to accommodate locally refined grids. This extension involves the advancement of the discrete system on a hierarchy of levels, each of which represents a degree of refinement, together with synchronization steps to ensure consistency across levels. A brief discussion of a software implementation is followed by a presentation of numerical results.},

doi = {10.2172/16136},

journal = {},

number = ,

volume = ,

place = {United States},

year = {1997},

month = {1}

}