Relativistic Vlasov-Maxwell modelling using finite volumes and adaptive mesh refinement

  • Benjamin Svedung Wettervik
  • Timothy C. DuBois
  • Evangelos Siminos
  • Tünde Fülöp
Open Access
Regular Article

DOI: 10.1140/epjd/e2017-80102-2

Cite this article as:
Wettervik, B.S., DuBois, T.C., Siminos, E. et al. Eur. Phys. J. D (2017) 71: 157. doi:10.1140/epjd/e2017-80102-2
Part of the following topical collections:
  1. Topical Issue: Relativistic Laser Plasma Interactions


The dynamics of collisionless plasmas can be modelled by the Vlasov-Maxwell system of equations. An Eulerian approach is needed to accurately describe processes that are governed by high energy tails in the distribution function, but is of limited efficiency for high dimensional problems. The use of an adaptive mesh can reduce the scaling of the computational cost with the dimension of the problem. Here, we present a relativistic Eulerian Vlasov-Maxwell solver with block-structured adaptive mesh refinement in one spatial and one momentum dimension. The discretization of the Vlasov equation is based on a high-order finite volume method. A flux corrected transport algorithm is applied to limit spurious oscillations and ensure the physical character of the distribution function. We demonstrate a speed-up by a factor of 7 × in a typical scenario involving laser pulse interaction with an underdense plasma due to the use of an adaptive mesh.

Graphical abstract

Copyright information

© The Author(s) 2017

Open Access This is an open access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  1. 1.Department of PhysicsChalmers University of TechnologyGothenburgSweden

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