# High-order nodal discontinuous Galerkin particle-in-cell method on unstructured grids

## Abstract

We present a high-order particle-in-cell (PIC) algorithm for the simulation of kinetic plasmas dynamics. The core of the algorithm utilizes an unstructured grid discontinuous Galerkin Maxwell field solver combining high-order accuracy with geometric flexibility. We introduce algorithms in the Lagrangian framework that preserve the favorable properties of the field solver in the PIC solver. Fast full-order interpolation and effective search algorithms are used for tracking individual particles on the general grid and smooth particle shape functions are introduced to ensure low noise in the charge and current density. A pre-computed levelset distance function is employed to represent the geometry and facilitates complex particle-boundary interaction. To enforce charge conservation we consider two different techniques, one based on projection and one on hyperbolic cleaning. Both are found to work well, although the latter is found be too expensive when used with explicit time integration. Examples of simple plasma phenomena, e.g., plasma waves, instabilities, and Landau damping are shown to agree well with theoretical predictions and/or results found by other computational methods. We also discuss generic well known problems such as numerical Cherenkov radiation and grid heating before presenting a few two-dimensional tests, showing the potential of the current method to handle fullymore »

- Authors:

- Division of Applied Mathematics, Brown University, Box F, Providence, RI 02912 (United States). E-mail: gjacobs2@dam.brown.edu
- Division of Applied Mathematics, Brown University, Box F, Providence, RI 02912 (United States). E-mail: Jan.Hesthaven@brown.edu

- Publication Date:

- OSTI Identifier:
- 20767040

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Computational Physics; Journal Volume: 214; Journal Issue: 1; Other Information: DOI: 10.1016/j.jcp.2005.09.008; PII: S0021-9991(05)00425-0; Copyright (c) 2005 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACCURACY; ALGORITHMS; CHARGE CONSERVATION; CHERENKOV RADIATION; CURRENT DENSITY; FORECASTING; GEOMETRY; INSTABILITY; INTERPOLATION; LAGRANGIAN FUNCTION; LANDAU DAMPING; MAXWELL EQUATIONS; NOISE; PLASMA WAVES; RELATIVISTIC PLASMA; SIMULATION; TWO-DIMENSIONAL CALCULATIONS

### Citation Formats

```
Jacobs, G.B., and Hesthaven, J.S.
```*High-order nodal discontinuous Galerkin particle-in-cell method on unstructured grids*. United States: N. p., 2006.
Web. doi:10.1016/j.jcp.2005.09.008.

```
Jacobs, G.B., & Hesthaven, J.S.
```*High-order nodal discontinuous Galerkin particle-in-cell method on unstructured grids*. United States. doi:10.1016/j.jcp.2005.09.008.

```
Jacobs, G.B., and Hesthaven, J.S. Mon .
"High-order nodal discontinuous Galerkin particle-in-cell method on unstructured grids". United States.
doi:10.1016/j.jcp.2005.09.008.
```

```
@article{osti_20767040,
```

title = {High-order nodal discontinuous Galerkin particle-in-cell method on unstructured grids},

author = {Jacobs, G.B. and Hesthaven, J.S.},

abstractNote = {We present a high-order particle-in-cell (PIC) algorithm for the simulation of kinetic plasmas dynamics. The core of the algorithm utilizes an unstructured grid discontinuous Galerkin Maxwell field solver combining high-order accuracy with geometric flexibility. We introduce algorithms in the Lagrangian framework that preserve the favorable properties of the field solver in the PIC solver. Fast full-order interpolation and effective search algorithms are used for tracking individual particles on the general grid and smooth particle shape functions are introduced to ensure low noise in the charge and current density. A pre-computed levelset distance function is employed to represent the geometry and facilitates complex particle-boundary interaction. To enforce charge conservation we consider two different techniques, one based on projection and one on hyperbolic cleaning. Both are found to work well, although the latter is found be too expensive when used with explicit time integration. Examples of simple plasma phenomena, e.g., plasma waves, instabilities, and Landau damping are shown to agree well with theoretical predictions and/or results found by other computational methods. We also discuss generic well known problems such as numerical Cherenkov radiation and grid heating before presenting a few two-dimensional tests, showing the potential of the current method to handle fully relativistic plasma dynamics in complex geometries.},

doi = {10.1016/j.jcp.2005.09.008},

journal = {Journal of Computational Physics},

number = 1,

volume = 214,

place = {United States},

year = {Mon May 01 00:00:00 EDT 2006},

month = {Mon May 01 00:00:00 EDT 2006}

}