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A semi-implicit fully Eulerian WENO scheme for high-fidelity Vlasov–Ampère simulations
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DOI：10.1016/j.cpc.2026.110292.png)
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Abstract
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High-fidelity kinetic plasma simulations demand numerical schemes that preserve fine phase-space structures while remaining stable over long integration times. Explicit Eulerian Vlasov solvers are constrained by stringent Courant–Friedrichs–Lewy (CFL) limits, whereas fully implicit approaches often require costly global matrix inversions. Here we present a semi-implicit, fully Eulerian unsplit solver for the 1D1V (One-Dimensional in Space and One-Dimensional in Velocity) Vlasov–Ampère system that relaxes the CFL constraint and improves parallel efficiency by avoiding matrix inversion and operator splitting. Phase-space derivatives are discretized using classical fifth-order WENO reconstruction, while the current in Ampère’s law is evaluated with high-accuracy cubic-spline integration. Time advancement employs a fourth-order Adams–Bashforth/Adams–Moulton predictor–corrector iteration to enable stable long-time evolution with minimal numerical error accumulation. The method accurately reproduces weak and strong Landau damping and captures both linear growth and nonlinear phase-space trapping in electron–electron and ion–ion two-stream instabilities, while maintaining small conservation errors without spurious numerical diffusion. Iteration and cost analyses identify an efficient operating regime near CFL ≃ 1. Strong-scaling benchmarks on Taiwania 3 using a hybrid MPI–OpenMP implementation demonstrate near-ideal scalability, supporting the proposed scheme as an efficient and robust framework for long-time, high-fidelity Eulerian Vlasov simulations.
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