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

TL;DR

This paper introduces a multiscale parallel-in-time method combining fluid and kinetic solvers to efficiently simulate the collisional Vlasov equation across various regimes, significantly reducing computational costs.

Contribution

The paper develops a novel multiscale parareal method that integrates fluid and kinetic solvers for efficient kinetic equation simulations in the fluid regime.

Findings

Demonstrates accuracy across multiple kinetic regimes

Achieves significant computational speedup

Validates approach with 1D-3D simulations

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.