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arXiv · 2502.02704

A Parareal in time numerical method for the collisional Vlasov equation in the hyperbolic scaling

Tino Laidin·Thomas Rey
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Abstract

We present the design of a multiscale parareal method for kinetic equations in the fluid dynamic regime. The goal is to reduce the cost of a fully kinetic simulation using a parallel in time procedure. Using the multiscale property of kinetic models, the cheap, coarse propagator consists in a fluid solver and the fine (expensive) propagation is achieved through a kinetic solver for a collisional Vlasov equation. To validate our approach, we present simulations in the 1D in space, 3D in velocity settings over a wide range of initial data and kinetic regimes, showcasing the accuracy, efficiency, and the speedup capabilities of our method.

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Tino Laidin, Thomas Rey. 2025-02-04. A Parareal in time numerical method for the collisional Vlasov equation in the hyperbolic scaling. https://arxiv.org/abs/2502.02704

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