We consider a 1D-2V Vlasov–Fokker–Planck multi-species ionic description coupled to fluid electrons. We address temporal stiffness with implicit time stepping, suitably preconditioned. To address temperature disparity in time and space, we extend the conservative adaptive velocity-space discretization scheme proposed in [Taitano et al., J. Comput. Phys., 318, 391–420, (2016)] to a spatially inhomogeneous system. Here in this approach, we normalize the velocity-space coordinate to a temporally and spatially varying local characteristic speed per species. We explicitly consider the resulting inertial terms in the Vlasov equation, and derive a discrete formulation that conserves mass, momentum, and energy up to a prescribed nonlinear tolerance upon convergence. Our conservation strategy employs nonlinear constraints to enforce these properties discretely for both the Vlasov operator and the Fokker–Planck collision operator. Numerical examples of varying degrees of complexity, including shock-wave propagation, demonstrate the favorable efficiency and accuracy properties of the scheme.

- Publication Date:

- Report Number(s):
- LA-UR-17-26086

Journal ID: ISSN 0021-9991

- Grant/Contract Number:
- AC52-06NA25396

- Type:
- Accepted Manuscript

- Journal Name:
- Journal of Computational Physics

- Additional Journal Information:
- Journal Volume: 365; 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 Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Conservative discretization; Thermal velocity based adaptive grid; 1D2V; Fokker–Planck; Rosenbluth potentials

- OSTI Identifier:
- 1469536

```
Taitano, William T., Chacon, Luis, and Simakov, Andrei N..
```*An adaptive, implicit, conservative, 1D-2V multi-species Vlasov–Fokker–Planck multi-scale solver in planar geometry*. United States: N. p.,
Web. doi:10.1016/j.jcp.2018.03.007.

```
Taitano, William T., Chacon, Luis, & Simakov, Andrei N..
```*An adaptive, implicit, conservative, 1D-2V multi-species Vlasov–Fokker–Planck multi-scale solver in planar geometry*. United States. doi:10.1016/j.jcp.2018.03.007.

```
Taitano, William T., Chacon, Luis, and Simakov, Andrei N.. 2018.
"An adaptive, implicit, conservative, 1D-2V multi-species Vlasov–Fokker–Planck multi-scale solver in planar geometry". United States.
doi:10.1016/j.jcp.2018.03.007. https://www.osti.gov/servlets/purl/1469536.
```

```
@article{osti_1469536,
```

title = {An adaptive, implicit, conservative, 1D-2V multi-species Vlasov–Fokker–Planck multi-scale solver in planar geometry},

author = {Taitano, William T. and Chacon, Luis and Simakov, Andrei N.},

abstractNote = {We consider a 1D-2V Vlasov–Fokker–Planck multi-species ionic description coupled to fluid electrons. We address temporal stiffness with implicit time stepping, suitably preconditioned. To address temperature disparity in time and space, we extend the conservative adaptive velocity-space discretization scheme proposed in [Taitano et al., J. Comput. Phys., 318, 391–420, (2016)] to a spatially inhomogeneous system. Here in this approach, we normalize the velocity-space coordinate to a temporally and spatially varying local characteristic speed per species. We explicitly consider the resulting inertial terms in the Vlasov equation, and derive a discrete formulation that conserves mass, momentum, and energy up to a prescribed nonlinear tolerance upon convergence. Our conservation strategy employs nonlinear constraints to enforce these properties discretely for both the Vlasov operator and the Fokker–Planck collision operator. Numerical examples of varying degrees of complexity, including shock-wave propagation, demonstrate the favorable efficiency and accuracy properties of the scheme.},

doi = {10.1016/j.jcp.2018.03.007},

journal = {Journal of Computational Physics},

number = C,

volume = 365,

place = {United States},

year = {2018},

month = {4}

}