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<p>A numerical dynamical low-rank approximation (DLRA) scheme for the solution of the Vlasov–Poisson equation is presented. Based on the formulation of the DLRA equations as Friedrichs’ systems in a continuous setting, it combines recently proposed conservative DLRA methods with a discontinuous Galerkin discretization. The resulting scheme is shown to ensure mass and momentum conservation at the discrete level. In addition, a new formulation of the conservative integrator is proposed based on its interpretation as a tangent space projector splitting scheme. Numerical experiments validate our approach in one- and two-dimensional simulations of Landau damping. As a demonstration of feasibility, it is also shown that the rank-adaptive unconventional integrator can be combined with mesh adaptivity.</p>

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Discontinuous Galerkin discretization of conservative dynamical low-rank approximation schemes for the Vlasov–Poisson equation

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月9日

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  • André Uschmajew,
  • Andreas Zeiser

摘要

A numerical dynamical low-rank approximation (DLRA) scheme for the solution of the Vlasov–Poisson equation is presented. Based on the formulation of the DLRA equations as Friedrichs’ systems in a continuous setting, it combines recently proposed conservative DLRA methods with a discontinuous Galerkin discretization. The resulting scheme is shown to ensure mass and momentum conservation at the discrete level. In addition, a new formulation of the conservative integrator is proposed based on its interpretation as a tangent space projector splitting scheme. Numerical experiments validate our approach in one- and two-dimensional simulations of Landau damping. As a demonstration of feasibility, it is also shown that the rank-adaptive unconventional integrator can be combined with mesh adaptivity.