### Abstract

Language | English |
---|---|

Article number | 100030 |

Number of pages | 19 |

Journal | Journal of Computational Physics: X |

Volume | 3 |

DOIs | |

State | Published - 4 Apr 2019 |

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### Keywords

- Liouville's equation, active flux scheme, geometric optics, hyperbolic conservation law, moving mesh

### Cite this

*Journal of Computational Physics: X*,

*3*, [100030]. DOI: 10.1016/j.jcpx.2019.100030

}

*Journal of Computational Physics: X*, vol. 3, 100030. DOI: 10.1016/j.jcpx.2019.100030

**Active flux schemes on moving meshes with applications to geometric optics.** / van Lith, Bart S. (Corresponding author); ten Thije Boonkkamp, Jan; IJzerman, Wilbert.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Active flux schemes on moving meshes with applications to geometric optics

AU - van Lith,Bart S.

AU - ten Thije Boonkkamp,Jan

AU - IJzerman,Wilbert

PY - 2019/4/4

Y1 - 2019/4/4

N2 - Active flux schemes are finite volume schemes that keep track of both point values and averages. The point values are updated using a sem-Langrangian step, making active flux schemes highly suitable for geometric optics problems on phase space, i.e., to solve Liouville's equation. We use a semi-discrete version of the active flux scheme. Curved optics lead to moving boundaries in phase space. Therefore, we introduce a novel way of defining the active flux scheme on moving meshes. We show, using scaling arguments as well as numerical experiments, that our scheme outperforms the current industry standard, ray tracing. It has higher accuracy as well as a more favourable time scaling. The numerical experiments demonstrate that the active flux scheme is orders of magnitude more accurate and faster than ray tracing.

AB - Active flux schemes are finite volume schemes that keep track of both point values and averages. The point values are updated using a sem-Langrangian step, making active flux schemes highly suitable for geometric optics problems on phase space, i.e., to solve Liouville's equation. We use a semi-discrete version of the active flux scheme. Curved optics lead to moving boundaries in phase space. Therefore, we introduce a novel way of defining the active flux scheme on moving meshes. We show, using scaling arguments as well as numerical experiments, that our scheme outperforms the current industry standard, ray tracing. It has higher accuracy as well as a more favourable time scaling. The numerical experiments demonstrate that the active flux scheme is orders of magnitude more accurate and faster than ray tracing.

KW - Liouville's equation, active flux scheme, geometric optics, hyperbolic conservation law, moving mesh

U2 - 10.1016/j.jcpx.2019.100030

DO - 10.1016/j.jcpx.2019.100030

M3 - Article

VL - 3

JO - Journal of Computational Physics: X

T2 - Journal of Computational Physics: X

JF - Journal of Computational Physics: X

SN - 2590-0552

M1 - 100030

ER -