Work

A second-order structure- and positivity-preserving convex limiting method for the Vlasov equations

Year: 2026

Type: preprint

Abstract: In this paper, we introduce a novel second-order, positivity-preserving finite element method for the Vlasov equations using a convex limiting algorithm. The method employs strong-stability-preserving (SSP) Runge-Kutta time integration and a tensor-product construction of the phase-space mesh for efficient high-dimensional implementations. The convex limiting algorithm combines the robust first-order positivity-preserving graph viscosity approach with high-order residual-based viscosity stabilization to obtain a high-order positivity-preserving scheme. Both novel first-order and high-order methods applicable to high-dimensional problems such as the Vlasov system are presented. In addition, we propose a divergence-cleaning technique for Maxwell's equations to ensure that the divergence constraints of the electromagnetic fields are satisfied. Numerical experiments are provided to demonstrate the accuracy and robustness of the proposed methods.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.28412

Authors: Kormann, Katharina, Nazarov, Murtazo, Wen, Junjie

Institutions: Ruhr University Bochum, Uppsala University

Language: English

Topic: Computational Fluid Dynamics and Aerodynamics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: Deutsche Forschungsgemeinschaft, Vetenskapsrådet, Uppsala Multidisciplinary Center for Advanced Computational Science

Awards: Geometric low-rank tensors and their application for noise reduction of kinetic particle simulations (gemTENS), Niedrigrangapproximation der Lösung von kinetischen ZweiTeilchenGleichungen, High fidelity modeling of fusion processes

OpenAlex ID: W7214145400

Cites: 32

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