2025/12/01 by Takashi Minoshima, Minoshima, Takashi, Yosuke Matsumoto +1
Mathematics · Physics and Astronomy · Engineering · #Gas Dynamics and Kinetic Theory #Model Reduction and Neural Networks #Advanced Numerical Methods in Computational Mathematics
paper · pdf · doi:10.48550/arxiv.2512.01322
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.