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arXiv · 2512.01322

A high-order weighted positive and flux conservative method for the Vlasov equation

Takashi Minoshima·Yosuke Matsumoto
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Abstract

We present a high-order conservative, positivity-preserving, and non-oscillatory scheme for solving the Vlasov equation. The scheme attains formal fifth-order accuracy through a convex combination of positive and non-oscillatory polynomials in substencils. Nonlinear weights for these polynomials are formulated that assign higher priority to substencils with larger L2 norm to enhance resolution while maintaining positivity and non-oscillatory properties. An approximate dispersion relation indicates that the spectral properties of the present scheme outperform those of an underlying fifth-order scheme and even surpass those of a seventh-order scheme in certain wavenumber ranges. We apply this scheme to the one-dimensional Vlasov-Ampere equations and the two-dimensional Vlasov-Maxwell equations, and demonstrate high-resolution simulations with improved conservation of entropy.

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Takashi Minoshima, Yosuke Matsumoto. 2025-12-01. A high-order weighted positive and flux conservative method for the Vlasov equation. https://arxiv.org/abs/2512.01322

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