### A curvilinear, fully implicit, conservative electromagnetic PIC algorithm in multiple dimensions

Here, we extend a recently proposed fully implicit PIC algorithm for the Vlasov–Darwin model in multiple dimensions (Chen and Chacón (2015) [1]) to curvilinear geometry. As in the Cartesian case, the approach is based on a potential formulation (Φ, A), and overcomes many difficulties of traditional semi-implicit Darwin PIC algorithms. Conservation theorems for local charge and global energy are derived in curvilinear representation, and then enforced discretely by a careful choice of the discretization of field and particle equations. Additionally, the algorithm conserves canonical-momentum in any ignorable direction, and preserves the Coulomb gauge ∇ • A = 0 exactly. An asymptotically well-posed fluid preconditioner allows efficient use of large cell sizes, which are determined by accuracy considerations, not stability, and can be orders of magnitude larger than required in a standard explicit electromagnetic PIC simulation. We demonstrate the accuracy and efficiency properties of the algorithm with numerical experiments in mapped meshes in 1D-3V and 2D-3V.

- Publication Date:

- Report Number(s):
- LA-UR-15-27639

Journal ID: ISSN 0021-9991

- Grant/Contract Number:
- AC52-06NA25396

- Type:
- Accepted Manuscript

- Journal Name:
- Journal of Computational Physics

- Additional Journal Information:
- Journal Volume: 316; Journal Issue: C; Journal ID: ISSN 0021-9991

- Publisher:
- Elsevier

- Research Org:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org:
- USDOE

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Mathematics; Magnetic Fusion Energy

- OSTI Identifier:
- 1255248

- Alternate Identifier(s):
- OSTI ID: 1348010

```
Chacon, L., and Chen, G..
```*A curvilinear, fully implicit, conservative electromagnetic PIC algorithm in multiple dimensions*. United States: N. p.,
Web. doi:10.1016/j.jcp.2016.03.070.

```
Chacon, L., & Chen, G..
```*A curvilinear, fully implicit, conservative electromagnetic PIC algorithm in multiple dimensions*. United States. doi:10.1016/j.jcp.2016.03.070.

```
Chacon, L., and Chen, G.. 2016.
"A curvilinear, fully implicit, conservative electromagnetic PIC algorithm in multiple dimensions". United States.
doi:10.1016/j.jcp.2016.03.070. https://www.osti.gov/servlets/purl/1255248.
```

```
@article{osti_1255248,
```

title = {A curvilinear, fully implicit, conservative electromagnetic PIC algorithm in multiple dimensions},

author = {Chacon, L. and Chen, G.},

abstractNote = {Here, we extend a recently proposed fully implicit PIC algorithm for the Vlasov–Darwin model in multiple dimensions (Chen and Chacón (2015) [1]) to curvilinear geometry. As in the Cartesian case, the approach is based on a potential formulation (Φ, A), and overcomes many difficulties of traditional semi-implicit Darwin PIC algorithms. Conservation theorems for local charge and global energy are derived in curvilinear representation, and then enforced discretely by a careful choice of the discretization of field and particle equations. Additionally, the algorithm conserves canonical-momentum in any ignorable direction, and preserves the Coulomb gauge ∇ • A = 0 exactly. An asymptotically well-posed fluid preconditioner allows efficient use of large cell sizes, which are determined by accuracy considerations, not stability, and can be orders of magnitude larger than required in a standard explicit electromagnetic PIC simulation. We demonstrate the accuracy and efficiency properties of the algorithm with numerical experiments in mapped meshes in 1D-3V and 2D-3V.},

doi = {10.1016/j.jcp.2016.03.070},

journal = {Journal of Computational Physics},

number = C,

volume = 316,

place = {United States},

year = {2016},

month = {4}

}