Service interruption on Monday 11 July from 12:30 to 13:00: all the sites of the CCSD (HAL, EpiSciences, SciencesConf, AureHAL) will be inaccessible (network hardware connection).
Skip to Main content Skip to Navigation
Journal articles

Asymptotic preserving and time diminishing schemes for rarefied gas dynamic

Abstract : In this work, we introduce a new class of numerical schemes for rarefied gas dynamic problems described by collisional kinetic equations. The idea consists in reformulating the problem using a micro-macro decomposition and successively in solving the microscopic part by using asymptotic preserving Monte Carlo methods. We consider two types of decompositions, the first leading to the Euler system of gas dynamics while the second to the Navier-Stokes equations for the macroscopic part. In addition, the particle method which solves the microscopic part is designed in such a way that the global scheme becomes computationally less expensive as the solution approaches the equilibrium state as opposite to standard methods for kinetic equations which computational cost increases with the number of interactions. At the same time, the statistical error due to the particle part of the solution decreases as the system approach the equilibrium state. This causes the method to degenerate to the sole solution of the macroscopic hydrodynamic equations (Euler or Navier-Stokes) in the limit of infinite number of collisions. In a last part, we will show the behaviors of this new approach in comparisons to standard Monte Carlo techniques for solving the kinetic equation by testing it on different problems which typically arise in rarefied gas dynamic simulations.
Complete list of metadata

Cited literature [38 references]  Display  Hide  Download
Contributor : Nicolas Crouseilles Connect in order to contact the contributor
Submitted on : Friday, November 4, 2016 - 1:27:43 PM
Last modification on : Friday, May 20, 2022 - 9:04:52 AM
Long-term archiving on: : Sunday, February 5, 2017 - 2:13:21 PM


Files produced by the author(s)



Nicolas Crouseilles, Giacomo Dimarco, Mohammed Lemou. Asymptotic preserving and time diminishing schemes for rarefied gas dynamic. Kinetic and Related Models , AIMS, 2017, 10 (3), pp.643-668. ⟨10.3934/krm.2017026⟩. ⟨hal-01392412⟩



Record views


Files downloads